Tootfinder

Hausdorff dimension of the graph of the error-sum function of continued fractions
Min Woong Ahn
https://arxiv.org/abs/2507.16536 https://

Hausdorff dimension of the graph of the error-sum function of continued fractions
We study the unweighted error-sum function $\mathcal{E}(x) \coloneqq \sum_{n \geq 0} ( x- p_n(x)/q_n(x) )$, where $p_n(x)/q_n(x)$ is the $n$th convergent of the continued fraction expansion of $x \in \mathbb{R}$. We prove that the Hausdorff dimension of the graph of $\mathcal{E}$ is exactly $1$. Our proof is number-theoretic in nature and involves Möbius inversion, summation over coprime convergent denominators, and precise upper bounds derived via continued fraction recurrence relations. As a…

A new parametric observational study of $f(Q,B)$ gravity with modified chaplygin gas
Amit Samaddar, S. Surendra Singh
https://arxiv.org/abs/2507.14251 http…

A new parametric observational study of $f(Q,B)$ gravity with modified chaplygin gas
In this work, we explore the cosmological dynamics of a modified gravity framework based on the function $f(Q,B)=δQ^{2}+βB$, where $Q$ denotes the nonmetricity scalar and $B$ is the boundary term that relates $Q$ to the Ricci scalar. The matter sector is modeled using the Modified Chaplygin Gas (MCG) with the equation of state $p=Aρ-\frac{B}{ρ^α}$, allowing the model to interpolate between early-time matter behavior and late-time cosmic acceleration. By deriving an analytical expression fo…

Cassini-Catalan Determinants via Ramanujan's Theta Identity
Nagananda K G, Jong Sung Kim
https://arxiv.org/abs/2508.11877 https://arxiv.org/pdf/2508.11…

Cassini-Catalan Determinants via Ramanujan's Theta Identity
In this paper, we show that the classical Cassini and Catalan identities for Fibonacci numbers arise naturally from a single quadratic theta-function identity of Ramanujan. Expanding the identity $ψ(q)ψ(q^{3})=ψ(q^{4})φ(q^{6})+q\,φ(q^{2})ψ(q^{12})$ via the Jacobi triple product and equating coefficients yields the unified $q$-determinant $F_{n+r}(q)F_{n-r}(q)-F_{n}(q)^{2}=(-q)^{\,n-r}F_{r}(q)^{2}$, $n\ge r\ge 1$, where $ψ(q)$ and $φ(q)$ are Ramanujan's theta functions with $q$ a complex…

Beyond ReLU: Chebyshev-DQN for Enhanced Deep Q-Networks
Saman Yazdannik, Morteza Tayefi, Shamim Sanisales
https://arxiv.org/abs/2508.14536 https://arxiv.or…

Beyond ReLU: Chebyshev-DQN for Enhanced Deep Q-Networks
The performance of Deep Q-Networks (DQN) is critically dependent on the ability of its underlying neural network to accurately approximate the action-value function. Standard function approximators, such as multi-layer perceptrons, may struggle to efficiently represent the complex value landscapes inherent in many reinforcement learning problems. This paper introduces a novel architecture, the Chebyshev-DQN (Ch-DQN), which integrates a Chebyshev polynomial basis into the DQN framework to create…

On the quantum algebra $su_q(1,1)$ from a Special Function standpoint
R. Alvarez-Nodarse, A. Arenas-Gomez
https://arxiv.org/abs/2507.14100 https://

On the quantum algebra $su_q(1,1)$ from a Special Function standpoint
In this paper, we study the tensor product of two unitary irreducible representations, as well as the tensor product of a unitary irreducible representation with a finite-dimensional one, and determine the corresponding Clebsch-Gordan coefficients. Using von Neumann's projection operator method, we obtain an explicit representation of these coefficients, which allows us to express them as symmetric q-hypergeometric series. Finally, by leveraging the properties of the q-hypergeometric function, …

Quantum algebra approach to univariate and multivariate rational functions of $q$-Racah type
Wolter Groenevelt, Carel Wagenaar
https://arxiv.org/abs/2507.13483

Quantum algebra approach to univariate and multivariate rational functions of $q$-Racah type
In this paper, we study rational functions of $q$-Racah type and a multivariate extension, using representation theory of $\mathcal U_q(\mathfrak{sl}_2)$. Eigenfunctions of twisted primitive elements in $\mathcal U_q(\mathfrak{su}_2)$ can be expressed in terms of $q^{-1}$-Krawtchouk polynomials. Using this, we show that overlap coefficients of solutions of a generalized eigenvalue problem (GEVP) and an eigenvalue problem (EVP) can be expressed in terms of a rational function of $_4φ_3$-type. W…

On the Sum of Additive Characters and its Applications over Finite Fields
Maithri K., Shivarama K. N., Indira K. P
https://arxiv.org/abs/2506.16081 https:/…

On the Sum of Additive Characters and its Applications over Finite Fields
In this paper, we study the sum of additive characters over finite fields, with a focus on those of specified \(\mathbb{F}_q\)-Order. We establish a general formula for these character sums, providing an additive analogue to classical results previously known for multiplicative characters. As an application, we derive a Möbius function \(μ(g)\) for polynomials \(g \in \mathbb{F}_q[x]\), analogous to the integer Möbius function \(μ(n)\), and develop a characteristic function for \(k\)-normal…

Reconstruction Codes for Deletions and Insertions: Connection, Distinction, and Construction
Yubo Sun, Gennian Ge
https://arxiv.org/abs/2508.14386 https://…

Reconstruction Codes for Deletions and Insertions: Connection, Distinction, and Construction
Let $\mathcal{B}(\cdot)$ be an error ball function. A set of $q$-ary sequences of length $n$ is referred to as an \emph{$(n,q,N;\mathcal{B})$-reconstruction code} if each sequence $\boldsymbol{x}$ within this set can be uniquely reconstructed from any $N$ distinct elements within its error ball $\mathcal{B}(\boldsymbol{x})$. The main objective in this area is to determine or establish bounds for the minimum redundancy of $(n,q,N;\mathcal{B})$-reconstruction codes, denoted by $ρ(n,q,N;\mathcal{…

Black Hole Mass/Charge Relation and Weak No-hair Theorem Conjecture
Guan-Yi Lu, Meng-Nan Yang, H. Lu
https://arxiv.org/abs/2508.14158 https://arxiv.org/pdf…

Black Hole Mass/Charge Relation and Weak No-hair Theorem Conjecture
We consider Einstein gravity minimally coupled to two Maxwell fields and one dilaton scalar. We study the electrically-charged spherically-symmetric and static solutions that are asymptotic to Minkowski spacetime. General solutions are described by four independent parameters: mass $M$, two electric charges $(Q_1,Q_2)$ and the scalar charge $Σ$. For black holes, the scalar charge is not independent, but a function of $(M,Q_1,Q_2)$. We provide a set of formulae relating the mass to the charges,…

Stability of Gel'fand's inverse interior spectral problem for Schr\"odinger operators
Jinpeng Lu
https://arxiv.org/abs/2507.15560 https://

Stability of Gel'fand's inverse interior spectral problem for Schrödinger operators
We study Gel'fand's inverse interior spectral problem of determining a closed Riemannian manifold $(M,g)$ and a potential function $q$ from the knowledge of the eigenvalues $λ_j$ of the Schrödinger operator $-Δ_g + q$ and the restriction of the eigenfunctions $ϕ_j|_U$ on a given open subset $U\subset M$, where $Δ_g$ is the Laplace-Beltrami operator on $(M,g)$. We prove that an approximation of finitely many spectral data on $U$ determines a finite metric space that is close to $(M,g)$…

Slow convergence of Birkhoff ergodic averages
Valery V. Ryzhikov
https://arxiv.org/abs/2507.16740 https://arxiv.org/pdf/2507.16740

Slow convergence of Birkhoff ergodic averages
Let $\{T^z\}$ be an ergodic action of the group $Z^n$ by automorphisms of the probability space $(X,m)$, $\sum_{i}^\infty a_i<\infty$, $a_i>0$. For any sequence $M_k\to +\infty$ there exist $N_k>M_k$ and a function $ f\in L_1(X,m)$ such that $$m\left(\ x:\ \left|\, A(x,N_k,f) - \int f \, dm\, \right|\ >\ a_k \ \right)\ \to\ 1,$$ where $$A(x,N,f) =\frac 1 {N^n} \sum_{z\in Q_N} f(T^{z}x),$$ $$Q_N=\{(z_1,\dots,z_n)\}\, :\, 1\leq z_1,\dots,z_n\leq N\}.$$

Eigenvalue Distribution of Large Weighted Random Sparse Uniform $q$-Hypergraphs
Valentin Vengerovsky
https://arxiv.org/abs/2508.13297 https://arxiv.org/pdf…

Eigenvalue Distribution of Large Weighted Random Sparse Uniform $q$-Hypergraphs
We study eigenvalue distribution of the adjacency matrix $A^{(N,p,q)}$ of weighted random uniform $q$-hypergraphs $Γ= Γ_{N,p,q}$. We assume that the graphs have $N$ vertices and the average number of hyperedges attached to one vertex is $(q-1)!\cdot p$. To each edge of the graph $e_{ij}$ we assign a weight given by a random variable $a_{ij}$ with all moments finite. We consider the moments of normalized eigenvalue counting function $σ_{N,p,q}$ of $A^{(N,p,q)}$. Assuming all moments of $a$ fi…

Description using equilibrium temperature in the canonical ensemble within the framework of the Tsallis statistics with the conventional expectation value
Masamichi Ishihara
https://arxiv.org/abs/2507.15258

Description using equilibrium temperature in the canonical ensemble within the framework of the Tsallis statistics with the conventional expectation value
We studied the thermodynamic quantities and the probability distribution, expressing the probability distribution as a function of the energy, in the canonical ensemble within the framework of the Tsallis statistics, which is characterized by the entropic parameter $q$, with the conventional expectation value. We treat the power-law-like distribution. The equilibrium temperature, which is often called the physical temperature, is employed to describe the probability distribution. The Tsallis st…

Dirichlet $L$-functions on the Critical Line
Sami Vihko
https://arxiv.org/abs/2506.16115 https://arxiv.org/pdf/2506.16115

Dirichlet $L$-functions on the Critical Line
In this paper we prove that the Dirichlet $L$-functions $L(1/2+ix,χ_q)$, where $χ_q$ is uniformly random Dirichlet character modulo $q$, converges to a random Schwartz distribution $ζ_{\mathrm{rand}}$, which is related to (complex) Gaussian multiplicative chaos. This is the same limiting object that appeared in [34], where the authors proved that the random shifts of the Riemann zeta function on the critical line $ζ(1/2+ix+iωT)$, where $ω\sim \mathrm{Unif} ([0,1])$ and $x\in \mathbb{R}$, …

Optimal Convergence Rates of Deep Neural Network Classifiers
Zihan Zhang, Lei Shi, Ding-Xuan Zhou
https://arxiv.org/abs/2506.14899 https://

Optimal Convergence Rates of Deep Neural Network Classifiers
In this paper, we study the binary classification problem on $[0,1]^d$ under the Tsybakov noise condition (with exponent $s \in [0,\infty]$) and the compositional assumption. This assumption requires the conditional class probability function of the data distribution to be the composition of $q+1$ vector-valued multivariate functions, where each component function is either a maximum value function or a Hölder-$β$ smooth function that depends only on $d_*$ of its input variables. Notably, $d_…

On $q$-real and $q$-complex numbers
Pavel Etingof
https://arxiv.org/abs/2508.08440 https://arxiv.org/pdf/2508.08440…

On $q$-real and $q$-complex numbers
In arXiv:1812.00170, S. Morier-Genoud and V. Ovsienko introduced the notion of the $q$-rational number $[x]_q$, $x\in \Bbb Q$, a rational function specializing to $x$ at $q=1$, obtained by $q$-deforming the continued fraction expansion of $x$. In arXiv:1908.04365 they introduced $q$-real numbers $[x]_q$, $x\in \Bbb R$ - a Laurent series in $q$ converging to the rational function $[x]_q$ when $x\in \Bbb Q$. In arXiv:2102.00891 it is proved that if $x\in \Bbb Q_{>1}$ then the series $[x]_q$ conve…

Global $q$-dependent inverse transforms of intensity autocorrelation data
Tobias Eklund, Christina M. Tonauer, Felix Lehmk\"uhler, Katrin Amann-Winkel
https://arxiv.org/abs/2507.14106

Global $q$-dependent inverse transforms of intensity autocorrelation data
We present a new analysis approach for intensity autocorrelation data, as measured with dynamic light scattering and X-ray photon correlation spectroscopy. Our analysis generalizes the established CONTIN and MULTIQ methods by direct nonlinear modeling of the $g_2$ function, enabling decomposition of complex dynamics without a priori knowledge of experimental scaling factors. We describe the mathematical formulation, implementation details, and strategies for solution, as well as demonstrate dec…

Green's function and volume noncollapsing estimates for the K\"ahler-Ricci flow
Weiqi Zhang, Yashan Zhang
https://arxiv.org/abs/2508.13646 https://

Green's function and volume noncollapsing estimates for the Kähler-Ricci flow
We prove a local volume noncollapsing property for the long-time Kähler-Ricci flow on a minimal Kähler manifold, improving previous results of Guo-Phong-Song-Sturm, Guedj-Tô and Vu. Similar result is also proved for a twisted Kähler-Ricci flow on non-minimal Kähler manifolds. In the course of proof, we develop new Green's function estimates for a general Kähler family under the $L^{p>1}$ and $L^1(\log L)^{q>n}$ volume density conditions.

Vector valued weighted analogue of converse of Wiener-L\'evy theorem and applications to modulation spaces
Divyang G. Bhimani, Karishman B. Solanki
https://arxiv.org/abs/2507.16516

Vector valued weighted analogue of converse of Wiener-Lévy theorem and applications to modulation spaces
We shall prove a strong converse of the Wiener-Lévy theorem in weighted setting for Banach algebra valued functions. In fact, it is shown that if $ω$ is a weight on a discrete abelian group $G$, $\mathcal X$ is a unital commutative Banach algebra and if $F$ is a $\mathcal X-$valued function defined on $\mathbb C$ such that $T_F(f)=F\circ f \in A^q(Γ,\mathcal X)$ for all $f\in A^1_ω(Γ,\mathcal X)$, then $F$ must be real analytic. Its multivariate analogue and analogue for locally compact ab…

Bayesian Interpretation of Husimi Function and Wehrl Entropy
Chen Xu, Yiqi Yu, Peng Zhang
https://arxiv.org/abs/2507.08600 https://ar…

Bayesian Interpretation of Husimi Function and Wehrl Entropy
Husimi function (Q-function) of a quantum state is the distribution function of the density operator in the coherent state representation. It is widely used in theoretical research, such as in quantum optics. The Wehrl entropy is the Shannon entropy of the Husimi function, and is non-zero even for pure states. This entropy has been extensively studied in mathematical physics. Recent research also suggests a significant connection between the Wehrl entropy and many-body quantum entanglement in s…

A generalization of Deterministic Finite Automata related to discharging
John M. Campbell
https://arxiv.org/abs/2506.14072 https://ar…

A generalization of Deterministic Finite Automata related to discharging
Deterministic Finite Automata (DFAs) are of central importance in automata theory. In view of how state diagrams for DFAs are defined using directed graphs, this leads us to introduce a generalization of DFAs related to a method widely used in graph theory referred to as the discharging method. Given a DFA $(Q, Σ, δ, q_{0}, F)$, the transition function $δ\colon Q \times Σ\to Q$ determines a directed path in the corresponding state diagram based on an input string $a_{1} a_{2} \cdots a_{n}$ …

Bounded $H^\infty$-calculus for vectorial-valued operators with Gaussian kernel estimates
Davide Addona, Vincenzo Leone, Luca Lorenzi, Abdelaziz Rhandi
https://arxiv.org/abs/2507.16368

Bounded $H^\infty$-calculus for vectorial-valued operators with Gaussian kernel estimates
We prove that the vector-valued generator of a bounded holomorphic semigroup represented by a kernel satisfying Gaussian estimates with bounded $H^\infty$-calculus in $L^2(\mathbb R^d;\mathbb C^m)$ admits bounded $H^\infty$-calculus for every $p\in (1,\infty)$. We apply this result to the elliptic operator $-{\rm div}(Q\nabla)+V$, where the potential term V is a matrix-valued function whose entries belong to $L^1_{\rm loc}(\mathbb R^d)$ and, for almost every $x\in \mathbb R^d$, $V(x)$ is a symm…

Explicit formulas of the relation between multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types
Naho Kawasaki
https://arxiv.org/abs/2507.15034 h…

Explicit formulas of the relation between multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types
Multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types are known as generalizations of the Riemann zeta function. In 2018, Kaneko and Tsumura proved that the multiple zeta functions of Arakawa-Kaneko type can be expressed as a ${\mathbb Q}$-linear combination of products of the ones of Euler-Zagier type and multiple zeta values. In this paper, we give explicit formulas to the above mentioned relation. Moreover, as a key of its proof, we also give certain functional equations among mul…

Dehn Sommerville Manifolds
Oliver Knill
https://arxiv.org/abs/2508.14372 https://arxiv.org/pdf/2508.14372

Dehn Sommerville Manifolds
Dehn-Sommerville manifolds are a class of finite abstract simplicial complexes that generalize discrete manifolds. Despite a simpler definition in comparison to manifolds, they still share most properties of manifolds. They especially satisfy all Dehn-Sommerville symmetries telling that half of the f-vector entries are redundant. They also share other properties with q-manifolds: for every Dehn-Sommerville q-manifold G and any function g: V(G) to A={0, ..., k} with positive k, the set of x such…

Bilateral $q$-ultraspherical functions
Michael J. Schlosser
https://arxiv.org/abs/2508.08908 https://arxiv.org/pdf/2508.08908

Bilateral $q$-ultraspherical functions
We introduce a bilateral extension of the continuous $q$-ultraspherical polynomials which we call bilateral $q$-ultraspherical functions. These functions are given as specific bilateral basic hypergeometric ${}_2ψ_2$ series, they are analytic in a variable $x=\cosθ$ and depend on two parameters $β$ and $γ$ and on a base $q$. For these bilateral $q$-ultraspherical functions we derive a bilateral generating function, find a three-term recurrence relation, explain how they behave under the act…

Logarithmic and Strong Coupling Models in Weyl-Type $f(Q,T)$ Gravity
Rahul Bhagat, S. K. Tripathy, B. Mishra
https://arxiv.org/abs/2506.13126 https://

Logarithmic and Strong Coupling Models in Weyl-Type $f(Q,T)$ Gravity
In this paper, we have explored the cosmological implications of Weyl-type $f(Q,T)$ gravity, a modified gravitational theory formulated from Weyl geometry. The nonmetricity scalar $Q$ is coupled to the trace $T$ of the energy-momentum tensor. We analyze two models based on the logarithmic and strong coupling form of the function $f(Q,T)$. The corresponding field equations are then solved numerically after reformulating the system in terms of redshift. We used combined dataset from Cosmic Chrono…

This https://arxiv.org/abs/2401.17852 has been replaced.
link: https://scholar.google.com/scholar?q=a

Theoretical smoothing frameworks for nonsmooth simple bilevel problems
Bilevel programming has recently received a great deal of attention due to its abundant applications in many areas. The optimal value function approach provides a useful reformulation of the bilevel problem, but its utility is often limited due to the nonsmoothness of the value function even in cases when the associated lower-level function is smooth. In this paper, we present two smoothing strategies for the value function associated with lower-level functions that are not necessarily smooth b…

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Dynamics of Vortex Clusters on a Torus
Aswathy K R, Udaya Maurya, Surya Teja Gavva, Rickmoy Samanta
https://arxiv.org/abs/2506.13158 https://

Dynamics of Vortex Clusters on a Torus
We investigate the collective dynamics of multivortex assemblies in a two dimensional (2D) toroidal fluid film of distinct curvature and topology. The incompressible and inviscid nature of the fluid allows a Hamiltonian description of the vortices, along with a self-force of geometric origin, arising from the standard Kirchhoff-Routh regularization procedure. The Hamiltonian dynamics is constructed in terms of $q$-digamma functions $Ψ_q(z)$, closely related to the Schottky-Klein prime function…

Generalized Schur partition functions and RG flows
Anirudh Deb, Shlomo S. Razamat
https://arxiv.org/abs/2506.13764 https://arxiv.org/…

Generalized Schur partition functions and RG flows
We revisit a double-scaled limit of the superconformal index of ${\cal N}=2$ superconformal field theories (SCFTs) which generalizes the Schur index. The resulting partition function, $\hat {\cal Z}(q,α)$, has a standard $q$-expansion with coefficients depending on a continuous parameter $α$. The Schur index is a special case with $α=1$. Through explicit computations we argue that this partition function is an invariant of certain mass deformations and vacuum expectation value (vev) deformat…

Nearly Optimal Bounds on the Fourier sampling numbers of Besov Spaces
Jonathan W. Siegel
https://arxiv.org/abs/2508.13991 https://arxiv.org/pdf/2508.13991

Nearly Optimal Bounds on the Fourier sampling numbers of Besov Spaces
Let $\mathbb{T}^d$ denote the $d$-dimensional torus. We consider the problem of optimally recovering a target function $f^*:\mathbb{T}^d\rightarrow \mathbb{C}$ from samples of its Fourier coefficients. We make classical smoothness assumptions on $f^*$, specifically that $f^*$ lies in a Besov space $B^s_\infty(L_q)$ with $s > 0$ and $1\leq q\leq \infty$, and measure recovery error in the $L_p$-norm with $1\leq p\leq \infty$. Abstractly, the optimal recovery error is characterized by a `restricte…

Non-isomorphic subfields of the BM and GGS maximal function fields
Peter Beelen, Tobias Drue, Maria Montanucci, Giovanni Zini
https://arxiv.org/abs/2506.20210

Non-isomorphic subfields of the BM and GGS maximal function fields
In 2016 Tafazolian et al. introduced new families of $\mathbb{F}_{q^{2n}}$-maximal function fields $\mathcal{Y}_{n,s}$ and $\mathcal{X}_{n,s,a,b}$ arising as subfields of the first generalized GK function field (GGS). In this way the authors found new examples of maximal function fields that are not isomorphic to subfields of the Hermitian function field. In this paper we construct analogous function fields $\tilde{\mathcal{Y}}_{n,s}$ and $\tilde{\mathcal{X}}_{n,s,a,b}$ as subfields of the seco…

Replaced article(s) found for q-bio.BM. https://arxiv.org/list/q-bio.BM/new/
[1/1]:
Function-Guided Conditional Generation Using Protein Language Models with Adapters

Ramanujan's partition generating functions modulo $\ell$
Kathrin Bringmann, William Craig, Ken Ono
https://arxiv.org/abs/2506.06101 https://

Ramanujan's partition generating functions modulo $\ell$
For the partition function $p(n)$, Ramanujan proved the striking identities $$ P_5(q):=\sum_{n\geq 0} p(5n+4)q^n =5\prod_{n\geq 1} \frac{\left(q^5;q^5\right)_{\infty}^5}{(q;q)_{\infty}^6}, $$ $$ P_7(q):=\sum_{n\geq 0} p(7n+5)q^n =7\prod_{n\geq 1}\frac{\left(q^7;q^7\right)_{\infty}^3}{(q;q)_{\infty}^4}+49q \prod_{n\geq 1}\frac{\left(q^7;q^7\right)_{\infty}^7}{(q;q)_{\infty}^8}, $$ where $(q;q)_{\infty}:=\prod_{n\geq 1}(1-q^n).$ As these identities imply his celebrated congruences modulo 5 …

Rectangular $C^1$-$Q_k$ Bell finite elements in two and three dimensions
Hongling Hu, Shangyou Zhang
https://arxiv.org/abs/2506.23702 https://

Rectangular $C^1$-$Q_k$ Bell finite elements in two and three dimensions
Both the function and its normal derivative on the element boundary are $Q_k$ polynomials for the Bogner-Fox-Schmit $C^1$-$Q_k$ finite element functions. Mathematically, to keep the optimal order of approximation, their spaces are required to include $P_k$ and $P_{k-1}$ polynomials respectively. We construct a Bell type $C^1$-$Q_k$ finite element on rectangular meshes in 2D and 3D, which has its normal derivative as a $Q_{k-1}$ polynomial on each face, for $k\ge 4$. We show, with a big re…

Generalized Samorodnitsky noisy function inequalities, with applications to error-correcting codes
Olakunle S. Abawonse, Jan Hazla, Ryan O'Donnell
https://arxiv.org/abs/2508.06940

Generalized Samorodnitsky noisy function inequalities, with applications to error-correcting codes
An inequality by Samorodnitsky states that if $f : \mathbb{F}_2^n \to \mathbb{R}$ is a nonnegative boolean function, and $S \subseteq [n]$ is chosen by randomly including each coordinate with probability a certain $λ= λ(q,ρ) < 1$, then \begin{equation} \log \|T_ρf\|_q \leq \mathbb{E}_{S} \log \|\mathbb{E}(f|S)\|_q\;. \end{equation} Samorodnitsky's inequality has several applications to the theory of error-correcting codes. Perhaps most notably, it can be used to s…

Theoretical Mass Function for Secondaries Forming via Gravitational Instability in Circumstellar Disks
Fred C. Adams, Aster G. Taylor, Michael R. Meyer
https://arxiv.org/abs/2508.09015

Theoretical Mass Function for Secondaries Forming via Gravitational Instability in Circumstellar Disks
This paper constructs a theoretical framework for calculating the distribution of masses for secondary bodies forming via gravitational instability in the outer regions of circumstellar disks. We show that several alternate ways to specify the mass scale of forming objects converge to the same result under the constraint that the parental disks are marginally stable with stability parameter $Q=1$. Next we show that the well-known constraint that the formation of secondary bodies requires rapid …

Role of non-extensivity $q$-parameter in tectonic seismic forecasting
Oscar Sotolongo-Costa, Miguel Eduardo Mora-Ramos
https://arxiv.org/abs/2508.04932 https://

Role of non-extensivity $q$-parameter in tectonic seismic forecasting
By writing total Tsallis entropy as a function of non-extensivity q-parameter withing the fragment-asperity model for earthquakes, a critical range of values is identified: 1.4

Primes in Arithmetic Progressions to Large Moduli and Siegel Zeroes
Thomas Wright
https://arxiv.org/abs/2507.10780 https://arxiv.org/…

Primes in Arithmetic Progressions to Large Moduli and Siegel Zeroes
Let $χ$ be a Dirichlet character mod $D$ with $L(s,χ)$ its associated $L$-function, and let $ψ(x,q,a)$ be Chebyshev's prime-counting function for primes congruent to $a$ modulo $q$. We that under the assumption of an exceptional character $χ$ with $L(1,χ)=o\left((\log D)^{-5}\right)$, for any $q

THIS👇👇👇👇👇
https://zirk.us/@ChrisMayLA6/114949958179517536
( And it highlights the fact that we need to rethink utilities, recognizing them as services necessary for a modern equitable society to function)

THIS👇👇👇👇👇
https://zirk.us/@ChrisMayLA6/114949958179517536
( And it highlights the fact that we need to rethink utilities, recognizing them as services necessary for a modern equitable society to function)

Conjugacy in fibre products, distortion, and the geometry of cyclic subgroups
Martin R Bridson
https://arxiv.org/abs/2507.17598 https://arxiv.org/pdf/2507.…

Conjugacy in fibre products, distortion, and the geometry of cyclic subgroups
We investigate the complexity of the conjugacy problem for fibre products in torsion-free hyperbolic groups. Let $G$ be a torsion-free hyperbolic group and let $P

This https://arxiv.org/abs/2212.12237 has been replaced.
link: https://scholar.google.com/scholar?q=a

Electron-phonon interaction and phonons in 2d doped semiconductors
Electron-phonon interaction and phonon frequencies of doped polar semiconductors are sensitive to long-range Coulomb forces and can be strongly affected by screening effects of free carriers, the latter changing significantly when approaching the two-dimensional limit. We tackle this problem within a linear-response dielectric-matrix formalism, where screening effects can be properly taken into account by generalized effective charge functions and the inverse scalar dielectric function, allowin…

Quasimodular forms arising from Jacobi's theta function and special symmetric polynomials
Tewodros Amdeberhan, Leonid G. Fel, Ken Ono
https://arxiv.org/abs/2507.12352

Quasimodular forms arising from Jacobi's theta function and special symmetric polynomials
Ramanujan derived a sequence of even weight $2n$ quasimodular forms $U_{2n}(q)$ from derivatives of Jacobi's weight $3/2$ theta function. Using the generating function for this sequence, one can construct sequences of quasimodular forms of all nonnegative integer weights with minimal input: a weight 1 modular form and a power series $F(X)$. Using the weight 1 form $θ(q)^2$ and $F(X)=e^{X/2}$, we obtain a sequence $\{Y_n(q)\}$ of weight $n$ quasimodular forms on $Γ_0(4)$ whose symmetric functi…

Replaced article(s) found for q-fin.TR. https://arxiv.org/list/q-fin.TR/new
[1/1]:
- Alternative Loss Function in Evaluation of Transformer Models
Jakub Micha\'nk\'ow, Pawe{\l} Sakowski, Robert \'Slepaczuk

Dynamical Systems with Bounded Condition and $C^{*}$-algebras
Takehiko Mori
https://arxiv.org/abs/2508.05713 https://arxiv.org/pdf/2508.05713

Dynamical Systems with Bounded Condition and $C^{*}$-algebras
By introducing the totally uniqueness condition for maps, we establish a one-to-one correspondence between the family of invariant sets for the $q x{+}d$-function (e.g. the $3 x{+}1$-map, also known as the Collatz map), where $q$ and $d$ are arbitrary positive odd numbers, and the family of reducing subspaces for the associated $C^{*}$-algebra. This extends the connection between the Collatz conjecture (also known as the $3 n{+}1$-problem) and the irreducibility of its associated $C^{*}$-algebr…

Inversions in parking functions
Kyle Celano, Jennifer Elder, Kimberly P. Hadaway, Pamela E. Harris, Amanda Priestley, Gabe Udell
https://arxiv.org/abs/2508.11587 https://…

Inversions in parking functions
In this paper, we obtain a q-exponential generating function for inversions on parking functions via symmetric function theory and also through a direct bijection to rooted labeled forests. We then apply these techniques to unit interval parking functions to give analogous results. We conclude by introducing a probabilistic approach through which we obtain formulas for the total number of inversions and several other statistics across all parking functions and other sets of words closed under r…

Searching for gluon saturation effects in momentum transfer dependence of coherent charmonium electroproduction off nuclei
J. Nemchik, J. \'Obertov\'a
https://arxiv.org/abs/2507.01531

Searching for gluon saturation effects in momentum transfer dependence of coherent charmonium electroproduction off nuclei
We study for the first time the transverse momentum transfer distributions $dσ/dt$ in coherent production of charmonia in nuclear ultra-peripheral and electron-ion collisions within the QCD color dipole approach based on a rigorous Green function formalism. This allows us to treat properly the color transparency effects, as well as the higher and leading-twist shadowing corrections associated with the $|Q\bar Q\rangle$ and $|Q\bar QnG\rangle$ Fock components of the photon. While the …

Essential norm and Schatten class of Hankel operators between weighted Fock spaces
Yi Liu, Yufeng Lu
https://arxiv.org/abs/2508.11882 https://arxiv.org/pdf…

Essential norm and Schatten class of Hankel operators between weighted Fock spaces
In this paper, we characterize the essential norm of Hankel operators from a weighted Fock space $F_φ^{p}$ to a weighted Lebesgue space $L_φ^{q}$ for all $1 \leq p, q < \infty$. Additionally, we characterize the Schatten-$h$ class membership for Hankel operators acting from $F_φ^{2}$ to $L_φ^{2}$, where the class is defined by a continuous increasing convex function $h$.

Robust estimation of optimal dynamic treatment regimes with nonignorable missing covariates
Jian Sun, Bo Fu, Li Su
https://arxiv.org/abs/2506.22892 https:/…

Robust estimation of optimal dynamic treatment regimes with nonignorable missing covariates
Estimating optimal dynamic treatment regimes (DTRs) using observational data is often challenged by nonignorable missing covariates arsing from informative monitoring of patients in clinical practice. To address nonignorable missingness of pseudo-outcomes induced by nonignorable missing covariates, a weighted Q-learning approach using parametric Q-function models and a semiparametric missingness propensity model has recently been proposed. However, misspecification of parametric Q-functions at …

This https://arxiv.org/abs/2409.10773 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Tight Lower Bounds under Asymmetric High-Order Hölder Smoothness and Uniform Convexity
In this paper, we provide tight lower bounds for the oracle complexity of minimizing high-order Hölder smooth and uniformly convex functions. Specifically, for a function whose $p^{th}$-order derivatives are Hölder continuous with degree $ν$ and parameter $H$, and that is uniformly convex with degree $q$ and parameter $σ$, we focus on two asymmetric cases: (1) $q > p + ν$, and (2) $q < p+ν$. Given up to $p^{th}$-order oracle access, we establish worst-case oracle complexities of $Ω\left(…

An interpolation of Bradley's sum formula
Anju Yokoi
https://arxiv.org/abs/2508.13254 https://arxiv.org/pdf/2508.13254…

An interpolation of Bradley's sum formula
The sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.

On compact sets possessing $q$-convex functions
Thomas Pawlaschyk, Nikolay Shcherbina
https://arxiv.org/abs/2505.24588 https://arxiv.…

On compact sets possessing $q$-convex functions
We show that there exists a $q$-convex function in a neighborhood of a compact set $K$ in a complex manifold $\mathcal{M}$ if and only if the $q$-nucleus of this compact set is empty. The latter can be characterized as the maximal $q$-pseudoconcave subset of $K$, i.e., a subset of $K$ containing all other compact $q$-pseudoconcave subsets in $K$.

Integer Partitions With Restricted Distinct Parts
Rinchin Drema, Nipen Saikia
https://arxiv.org/abs/2508.12739 https://arxiv.org/pdf/2508.12739

Integer Partitions With Restricted Distinct Parts
For any positive integers $s$ and $t$, let $Q_{t}^{s}(n)$ denotes the number of partitions of a positive integer $n$ into distinct parts such that no part is congruent to $s$ or $t-s$ modulo $t$. We prove some Ramanujan-type congruences for $Q_{t}^{s}(n)$ for some particular values of $s$ and $t$ by employing $q$-series and theta function identities.

Replaced article(s) found for q-bio.BM. https://arxiv.org/list/q-bio.BM/new
[1/1]:
- Into the Unknown: From Structure to Disorder in Protein Function Prediction
Kolari\'c, Chow, Zhu, Toth-Petroczy, Alderson, Priti\v{s}anac

Holographic F(Q,T) Gravity with Lambert Solution
Houda Filali, Mouhsine Koussou, Mohamed Bennai, Rachid Ahl Laamara
https://arxiv.org/abs/2508.03486 https://

Holographic F(Q,T) Gravity with Lambert Solution
In this work, we study a model of holographic dark energy using FLRW cosmology in the context of modified gravity. An extension of the symmetric teleparallel gravity is obtained by considering the gravitational action L is given by an arbitrary function f of the nonmetricity Q, where the nonmetricity Q is responsible for the gravitational interaction, and the trace of the matter energy momentum tensor T, so that L=f(Q,T). We expand on the features of the derived cosmological model in view of th…

This https://arxiv.org/abs/2312.00871 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

The q-Schwarzian and Liouville gravity
We present a new holographic duality between q-Schwarzian quantum mechanics and Liouville gravity. The q-Schwarzian is a one parameter deformation of the Schwarzian, which is dual to JT gravity and describes the low energy sector of SYK. We show that the q-Schwarzian in turn is dual to sinh dilaton gravity. This one parameter deformation of JT gravity can be rewritten as Liouville gravity. We match the thermodynamics and classical two point function between q-Schwarzian and Liouville gravity. W…

Spectral analysis of $q$-deformed unitary ensembles with the Al-Salam--Carlitz weight
Sung-Soo Byun, Yeong-Gwang Jung, Jaeseong Oh
https://arxiv.org/abs/2507.18042 https://

Spectral analysis of $q$-deformed unitary ensembles with the Al-Salam--Carlitz weight
We study $q$-deformed random unitary ensembles associated with the weight function of the Al-Salam--Carlitz orthogonal polynomials, indexed by a parameter $a < 0$. In the special case $a = -1$, the model reduces to the $q$-deformed Gaussian unitary ensemble. Employing the Flajolet--Viennot theory together with the combinatorics of matchings, we derive an explicit positive-sum expression for the spectral moments. In the double-scaling regime $q = e^{-λ/N}$, where $N$ denotes the ensemble size a…

Concentrating solutions of the fractional $(p,q)$-Choquard equation with exponential growth
Yueqiang Song, Xueqi Sun, Du\v{s}an D. Repov\v{s}
https://arxiv.org/abs/2506.00412

Concentrating solutions of the fractional $(p,q)$-Choquard equation with exponential growth
This article deals with the following fractional $(p,q)$-Choquard equation with exponential growth of the form: $$\varepsilon^{ps}(-Δ)_{p}^{s}u+\varepsilon^{qs}(-Δ)_q^su+ Z(x)(|u|^{p-2}u+|u|^{q-2}u)=\varepsilon^{μ-N}[|x|^{-μ}*F(u)]f(u) \ \ \mbox{in} \ \ \mathbb{R}^N,$$ where $s\in (0,1),$ $\varepsilon>0$ is a parameter, $2\leq p=\frac{N}{s}

Rational minimax approximation of matrix-valued functions
Lei-Hong Zhang, Ya-Nan Zhang, Chenkun Zhang, Shanheng Han
https://arxiv.org/abs/2508.06378 https://

Rational minimax approximation of matrix-valued functions
In this paper, we present a rigorous framework for rational minimax approximation of matrix-valued functions that generalizes classical scalar approximation theory. Given sampled data $\{(x_\ell, {F}(x_\ell))\}_{\ell=1}^m$ where ${F}:\mathbb{C} \to \mathbb{C}^{s \times t}$ is a matrix-valued function, we study the problem of finding a matrix-valued rational approximant ${R}(x) = {P}(x)/q(x)$ (with ${P}:\mathbb{C} \to \mathbb{C}^{s \times t}$ a matrix-valued polynomial and $q(x)$ a nonzero scala…

This https://arxiv.org/abs/2109.10887 has been replaced.
link: https://scholar.google.com/scholar?q=a

Asymptotic error in the eigenfunction expansion for the Green's function of a Sturm-Liouville problem
We study the asymptotic error arising when approximating the Green's function of a Sturm-Liouville problem through a truncation of its eigenfunction expansion, both for the Green's function of a regular Sturm-Liouville problem and for the Green's function associated with the Hermite polynomials, the associated Laguerre polynomials, and the Jacobi polynomials, respectively. We prove that the asymptotic error obtained on the diagonal can be expressed in terms of the coefficients of the related se…

On gap sets in arbitrary Kummer extensions of $K(x)$
Ethan Cotterill, Erik A. R. Mendoza, Pietro Speziali
https://arxiv.org/abs/2506.19169 https://

On gap sets in arbitrary Kummer extensions of $K(x)$
Let $K$ be an algebraically closed field, and let $F/K(x)$ be a Kummer extension of function fields of genus $g$. We provide a compact and explicit description of the gap set $G(Q)$ at any totally ramified place $Q$ of the extension $F/K(x)$. As a consequence, we deduce structural properties of the Weierstrass semigroup $H(Q)$; in particular, we determine a generating set for $H(Q)$, and we characterize its symmetry in certain cases. We also generalize a formula due to Towse that describes the …

Convolutive sequences, I: Through the lens of integer partition functions
Shane Chern, Dennis Eichhorn, Shishuo Fu, James A. Sellers
https://arxiv.org/abs/2507.10965

Convolutive sequences, I: Through the lens of integer partition functions
Motivated by the convolutive behavior of the counting function for partitions with designated summands in which all parts are odd, we consider coefficient sequences $(a_n)_{n\ge 0}$ of primitive eta-products that satisfy the generic convolutive property \begin{align*} \sum_{n\ge 0} a_{mn} q^n = \left(\sum_{n\ge 0} a_n q^n\right)^m \end{align*} for a specific positive integer $m$. Given the results of an exhaustive search of the Online Encyclopedia of Integer Sequences for such sequences…

Twisted second moment of primitive cubic L-functions
Ziwei Hong, Zhiyong Zheng
https://arxiv.org/abs/2506.14656 https://arxiv.org/pdf…

Twisted second moment of primitive cubic L-functions
We investigate the mean value of the twisted second moment of primitive cubic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum \begin{equation*} \sum_{\substack{χ primitive\ cubic\\ genus(χ)=g}}χ(h_1)\barχ(h_2)|L_q(\frac{1}{2}, χ)|^2, \end{equation*} where $L_q(s,χ)$ denotes the $L$-function associated with primitive cubic character $χ$. Employing a double Dirichlet series approach, we establish an error term of size

This https://arxiv.org/abs/2310.12271 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Herz-Type Hardy Spaces Associated with Ball Quasi-Banach Function Spaces
Let $X$ be a ball quasi-Banach function space, $α\in \mathbb{R}$ and $q\in(0,\infty)$. In this paper, the authors first introduce the Herz-type Hardy space $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$, which is defined via the non-tangential grand maximal function. Under some mild assumptions on $X$, the authors establish the atomic decompositions of $\mathcal{H\dot{K}}_{X}^{α,\,q}({\mathbb {R}}^n)$. As an application, the authors obtain the boundedness of certain sublinear operators …

This https://arxiv.org/abs/2202.01956 has been replaced.
link: https://scholar.google.com/scholar?q=a

Maximum Likelihood Estimation of Optimal Receiver Operating Characteristic Curves from Likelihood Ratio Observations
The optimal receiver operating characteristic (ROC) curve, giving the maximum probability of detection as a function of the probability of false alarm, is a key information-theoretic indicator of the difficulty of a binary hypothesis testing problem (BHT). It is well known that the optimal ROC curve for a given BHT, corresponding to the likelihood ratio test, is determined by the probability distribution of the observed data under each of the two hypotheses. In some cases, these two distributio…

Cosmology with Distinct Functions $f$ of the Non-metricity Scalar $Q$ : A Dynamical System Approach
Promila Biswas, Subhajit Pal, Ritabrata Biswas, Satyajit Pal
https://arxiv.org/abs/2506.21646

Cosmology with Distinct Functions $f$ of the Non-metricity Scalar $Q$ : A Dynamical System Approach
Symmetric teleparallel gravity is one among the general relativistic trinity which deals with the non-metricity scalar $Q$. In the Einstein Hilbert action, a function of $Q$ is chosen to be the main contributory part of the Lagrangian and a modified theory of gravity is constructed. In literature, different structures of the function of $Q$ are found which sustain several astrophysical observations like Big Bang nucleosynthesis, late-time cosmic acceleration etc. Autonomous systems for each suc…

Nondegeneracy of positive solutions for critical Hartree equation on Heisenberg group and it's applications
Minbo Yang, Shuijin Zhang
https://arxiv.org/abs/2508.07719 https:…

Nondegeneracy of positive solutions for critical Hartree equation on Heisenberg group and it's applications
We study the uniqueness and nondegeneracy of positive bubble solutions for the generalized energy-critical Hartree equation on the Heisenberg group $\mathbb{H}^{n}$, \begin{equation}\label{0.1} -Δ_{\mathbb{H}}u=\left(\int_{\mathbb{H}^{n}}\frac{|u(η)|^{Q^{\ast}_μ}}{|η^{-1}ξ|^μ}\mathrm{d}η\right)|u|^{Q^{\ast}_μ-2}u,~~~ξ,η\in\mathbb{H}^{n}, \end{equation} where $Δ_{\mathbb{H}}$ represents the Kohn Laplacian, $u(η)$ is a real-valued function, $Q=2n+2$ is …

Descriptions of Cantor Sets: A Set-Theoretic Survey and Open Problems
Mohsen Soltanifar
https://arxiv.org/abs/2506.13103 https://arxi…

Descriptions of Cantor Sets: A Set-Theoretic Survey and Open Problems
This survey synthesizes the principal descriptive set-theoretic perspectives on deterministic Cantor sets on the real line and charts directions for future study. After recounting their historical genesis and compiling an up-to-date taxonomy, we review the Borel hierarchy and four hierarchically ordered representations-general, nested, iterated-function-system (IFS), and q-ary expansion-presented from the most general to the most specific set-theoretic description of deterministic Cantor sets. …

Cubic spline functions revisited
Florian Jarre
https://arxiv.org/abs/2507.05083 https://arxiv.org/pdf/2507.05083

Cubic spline functions revisited
In this paper a fourth order asymptotically optimal error bound for a new cubic interpolating spline function, denoted by Q-spline, is derived for the case that only function values at given points are used but not any derivative information. The bound seems to be stronger than earlier error bounds for cubic spline interpolation in such setting such as the not-a-knot spline. A brief analysis of the conditioning of the end conditions of cubic spline interpolation leads to a modification of the n…

The spaces of rational curves on del Pezzo surfaces via conic bundles
Sho Tanimoto
https://arxiv.org/abs/2506.18239 https://arxiv.org…

The spaces of rational curves on del Pezzo surfaces via conic bundles
Using the homological sieve method developed by Das--Lehmann--Tosteson and the author, we prove Peyre's all height approach to Manin's conjecture for split quintic del Pezzo surfaces defined over $\mathbb F_q(t)$ assuming $q$ is sufficiently large. We also establish lower bounds of correct magnitude for the counting function of rational curves on split low degree del Pezzo surfaces defined over $\mathbb F_q$ assuming $q$ is large.

This https://arxiv.org/abs/2204.07330 has been replaced.
link: https://scholar.google.com/scholar?q=a

Differentially Private Distributed Mismatch Tracking Algorithm for Constraint-Coupled Resource Allocation Problems
This paper considers privacy-concerned distributed constraint-coupled resource allocation problems over an undirected network, where each agent holds a private cost function and obtains the solution via only local communication. With privacy concerns, we mask the exchanged information with independent Laplace noise against a potential attacker with potential access to all network communications. We propose a differentially private distributed mismatch tracking algorithm (diff-DMAC) to achieve c…

Backbone colouring of chordal graphs
J\'ulio Ara\'ujo, Nicolas Nisse, Lucas Picasarri-Arrieta
https://arxiv.org/abs/2508.02980 https://arxiv.org/pd…

Backbone colouring of chordal graphs
A proper $k$-colouring of a graph $G=(V,E)$ is a function $c: V(G)\to \{1,\ldots,k\}$ such that $c(u)\neq c(v)$ for every edge $uv\in E(G)$. The chromatic number $χ(G)$ is the minimum $k$ such that there exists a proper $k$-colouring of $G$. Given a spanning subgraph $H$ of $G$, a $q$-backbone $k$-colouring of $(G,H)$ is a proper $k$-colouring $c$ of $G$ such that $\lvert c(u)-c(v)\rvert \ge q$ for every edge $uv\in E(H)$. The $q$-backbone chromatic number ${\rm BBC}_q(G,H)$ is the smallest $k…

The partition function and elliptic curves
Ken Ono
https://arxiv.org/abs/2508.09608 https://arxiv.org/pdf/2508.09608

The partition function and elliptic curves
We recast congruences for the partition function through the geometry of supersingular elliptic curves. For primes $\ell\ge5$ inert in $K_n=\mathbb{Q}(\sqrt{1-24n})$ (equivalently $\big(\tfrac{1-24n}{\ell}\big)=-1$), we show that $p(n)\pmod{\ell}$ is a "supersingular trace'' on $X_0(6)$: a computable dot product on the level-$6$ Brandt module that is a twisted analogue of the Deuring--Eichler formula for class numbers. In the ramified case $\ell\in\{5,7,11\}$ (i.e. $\ell\mid(1-24n)$), a geometr…

Monotonicity in half-spaces for singular quasilinear elliptic problems involving the gradient
Phuong Le
https://arxiv.org/abs/2508.08859 https://arxiv.org/…

Monotonicity in half-spaces for singular quasilinear elliptic problems involving the gradient
We study positive solutions to the problem $-Δ_p u + \vartheta |\nabla u|^q = \frac{1}{u^γ} + f(u)$ in $\mathbb{R}^N_+$ with the zero Dirichlet boundary condition, where $p>1$, $γ>0$, $0

This https://arxiv.org/abs/2210.12988 has been replaced.
link: https://scholar.google.com/scholar?q=a

Embeddings between generalized weighted Lorentz spaces
We give a new characterization of a continuous embedding between two function spaces of type $GΓ$. Such spaces are governed by functionals of type \begin{equation*} \|f\|_{GΓ(r,q;w,δ)} := \left(\int_{0}^{L} \left( \frac1{Δ(t)} \int_0^t f^*(s)^r δ(s) ds \right)^{\frac{q}{r}} w(t) dt \right)^\frac1{q}, \end{equation*} in which $f^*$ is the nonincreasing rearrangement of $f$, $L\in(0,\infty]$, $r,q \in (0, \infty)$, $w, δ$ are weights on $(0,L)$ and $Δ(t)=\int_{0}^{t}δ(s)\,ds$ fo…

This https://arxiv.org/abs/2404.17061 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Gauge origami and quiver W-algebras II: Vertex function and beyond quantum $q$-Langlands correspondence
We continue the study of generalized gauge theory called gauge origami, based on the quantum algebraic approach initiated in [arXiv:2310.08545]. In this article, we in particular explore the D2 brane system realized by the screened vertex operators of the corresponding W-algebra. The partition function of this system given by the corresponding conformal block is identified with the vertex function associated with quasimaps to Nakajima quiver varieties and generalizations, that plays a central r…

On the proportion of derangements in affine classical groups
Jessica Anzanello
https://arxiv.org/abs/2508.07093 https://arxiv.org/pdf/2508.07093

On the proportion of derangements in affine classical groups
We derive explicit formulas for the proportion of derangements and of derangements of $p$-power order in the affine unitary group $AU_m(q)$ over the finite field $\mathbb{F}_{q^2}$ of characteristic $p$. Both formulas rely on a result of independent interest concerning integer partitions: we obtain a generating function for partitions $λ=(λ_1, \dots, λ_m)$ into $m$ parts, for which $λ_1=1$ or there exists $k \in \{2, \dots,m\}$ such that $λ_{k-1}>λ_k=k$. Moreover, when $p$ is odd, we conj…

A Note on the Walsh Spectrum of Power Residue S-Boxes
Matthias Johann Steiner
https://arxiv.org/abs/2507.06808 https://arxiv.org/pdf/…

A Note on the Walsh Spectrum of Power Residue S-Boxes
Let $\mathbb{F}_q$ be a prime field with $q \geq 3$, and let $d, m \geq 1$ be integers such that $\gcd \left( d, q \right) = 1$ and $m \mid (q - 1)$. In this paper we bound the absolute values of the Walsh spectrum of S-Boxes $S (x) = x^d \cdot T \left( x^\frac{q - 1}{m} \right)$, where $T$ is a function with $T (x) \neq 0$ if $x \neq 0$. Such S-Boxes have been proposed for the Zero-Knowledge-friendly hash functions Grendel and Polocolo. In particular, we prove the conjectured correlation of th…

Counting edges of different types in a local graph of a Grassmann graph
Ian Seong
https://arxiv.org/abs/2506.18700 https://arxiv.org/…

Counting edges of different types in a local graph of a Grassmann graph
Let $\mathbb{F}_q$ denote a finite field with $q$ elements. Let $n,k$ denote integers with $n>2k\geq 6$. Let $V$ denote a vector space over $\mathbb{F}_{q}$ that has dimension $n$. The vertex set of the Grassmann graph $J_q(n,k)$ consists of the $k$-dimensional subspaces of $V$. Two vertices of $J_q(n,k)$ are adjacent whenever their intersection has dimension $k-1$. Let $\partial$ denote the path-length distance function of $J_q(n,k)$. Pick vertices $x,y$ of $J_q(n,k)$ such that $1<\partial(x,y…

This https://arxiv.org/abs/2207.11904 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the Tate conjecture for divisors on varieties with $h^{2,0} = 1$ in positive characteristics
We prove that the Tate conjecture for divisors is ''generically true'' for mod p reductions of complex projective varieties with $h^{2, 0} = 1$, under a mild assumption on moduli. By refining this general result, we establish a new case of the BSD conjecture over global function fields, and the Tate conjecture for a class of general type surfaces of geometric genus 1.

Boundary estimates for singular elliptic problems involving a gradient term
Phuong Le
https://arxiv.org/abs/2508.07360 https://arxiv.org/pdf/2508.07360

Boundary estimates for singular elliptic problems involving a gradient term
We study the behavior of weak solutions to the singular quasilinear elliptic problem $-Δ_p u + \vartheta |\nabla u|^q = \frac{1}{u^γ} + f(u)$, in a bounded domain with the Dirichlet boundary condition, where $p>1$, $γ>0$, $0

Lifting $L$-polynomials of genus 2 curves
Jia Shi
https://arxiv.org/abs/2508.11028 https://arxiv.org/pdf/2508.11028…

Lifting $L$-polynomials of genus 2 curves
Let $C$ be a genus $2$ curve over $\mathbb{Q}$. Harvey and Sutherland's implementation of Harvey's average polynomial-time algorithm computes the $\bmod \ p$ reduction of the numerator of the zeta function of $C$ at all good primes $p\leq B$ in $O(B\log^{3+o(1)}B)$ time, which is $O(\log^{4+o(1)} p)$ time on average per prime. Alternatively, their algorithm can do this for a single good prime $p$ in $O(p^{1/2}\log^{1+o(1)}p)$ time. While Harvey's algorithm can also be used to compute the full z…

Nonvanishing of $L$--functions associated to fixed order characters over function fields
Chantal David, Alexandra Florea, Matilde Lalin
https://arxiv.org/abs/2506.07815

Nonvanishing of $L$--functions associated to fixed order characters over function fields
We show that a positive proportion of the values $L(1/2,χ_c)$ are non-zero, where $χ_c$ is the $\ell^{\text{th}}$ residue symbol for $\ell \geq 3$ over $\mathbb{F}_q[t]$, when averaging over square-free polynomials $c$ in $\mathbb{F}_q[t]$, as $q \equiv 1(\textrm{mod}\,{2\ell})$ is fixed and the degree of $c$ goes to infinity. In the case of $\ell=3$, we show that at least $1/6$ of $L(1/2,χ_c)\neq 0$, while for $\ell>3$, the proportion depends on the order of the character. This improves a p…

Muckenhoupt-weighted $L_q(L_p)$ boundedness for time-space fractional nonlocal operators
Yong Zhen Yang, Yong Zhou
https://arxiv.org/abs/2507.01890 https:/…

Muckenhoupt-weighted $L_q(L_p)$ boundedness for time-space fractional nonlocal operators
Based on the $ϕ(Δ)$-type operator studied by Kim \cite[\emph{Adv.~Math.}]{Kim2}, where $ϕ$ is a Bernstein function, we establish weighted $L_{q}(L_{p})$ estimates for solutions to the following fractional evolution equation: $$ \partial_{t}^αw(t,x) = ϕ(Δ)w(t,x) + h(t,x), \quad t > 0, \; x \in \mathbb{R}^{d}, $$ where $\partial_{t}^α$ denotes the Caputo derivative of $0 < α< 1$. To be specific, for all $1 < p, q < \infty$, we demonstrate that $$ \int_{0}^{\infty} \left( \int_{\mathbb{R}^…

Parking functions and chip-firing on hypergraphs
Timothy Blanton, Anton Dochtermann, Isabelle Hong, SuHo Oh, Zhan Zhan
https://arxiv.org/abs/2508.09720 https://

Parking functions and chip-firing on hypergraphs
For a connected graph $G$ with sink vertex $q$, a $G$-parking function is a vector of nonnegative integers whose entries are determined by cut-sets in $G$. Such objects also arise as the superstable configurations in the context of chip-firing. The set of all $G$-parking functions have various algebraic and combinatorial properties; for instance they relate to evaluations of the Tutte polynomial and in particular are counted by spanning trees of $G$. We extend these constructions to the setting…

Generalized Brans-Dicke theory from Verlinde's entropic gravity
Salih Kibaro\u{g}lu, Mustafa Senay
https://arxiv.org/abs/2506.02729 https://

Generalized Brans-Dicke theory from Verlinde's entropic gravity
In this work, we develop a q-deformed scalar-tensor theory of gravitation by combining Verlinde's entropic gravity paradigm with statistical deformation effects. The resulting model modifies the Brans-Dicke framework through a deformation function, treated as a constant rescaling factor for the effective gravitational coupling. We derive the corresponding q-deformed field equations and analyze their theoretical consistency including the recovery of standard gravitational models in specific limi…

Counting w-coprime S-integers and S-integral ideals in positive characteristic
Si-Han Liu, Zhe-Cheng Liu, Jia-Yan Yao
https://arxiv.org/abs/2508.10484 https://

Counting w-coprime S-integers and S-integral ideals in positive characteristic
Let Fq be the finite field with q elements, and K an algebraic function field over with Fq as its field of constants. Let S be a finite nonempty set of prime divisors over K, and OS be the ring of integers of K attached to S. Let w greater than 1 be an integer. In this work we shall count w coprime S integers and S integral ideals, and our proofs are a combination of analytic methods and the Riemann Roch theorem and the Weil theorem for function fields in positive characteristic.

Algorithm for computing the partition function of the Potts model for SP-graphs
Sofya Mukhamedzhanova, Bulat Sabirov, Amir Mukhamedzhanov
https://arxiv.org/abs/2507.22579 https:…

Algorithm for computing the partition function of the Potts model for SP-graphs
The q-state Potts model is a fundamental framework in statistical physics and graph theory, with its partition function encoding rich information about spin configurations. The multivariate Tutte polynomial (known as the partition function of the Potts model) can be defined on an arbitrary finite graph $G$ and encodes a lot of important combinatorial information about the graph. As a special case, it contains the familiar Tutte polynomial with two variables and, consequently, its specialization…

Conformal Green functions and Yamabe metrics of Sobolev regularity
Rodrigo Avalos, Albachiara Cogo, Andoni Royo Abrego
https://arxiv.org/abs/2507.01674 htt…

Conformal Green functions and Yamabe metrics of Sobolev regularity
We provide a full resolution of the Yamabe problem on closed 3-manifolds for Riemannian metrics of Sobolev class $W^{2,q}$ with $q > 3$. This requires developing an elliptic theory for the conformal Laplacian for rough metrics and establishing existence, regularity and a delicate blow-up analysis for its Green function. Most of the analytical work is carried out in dimensions $n \geq 3$ and for $W^{2,q}$ Riemannian metrics with $q>\tfrac{n}{2}$ and should be of independent interest.

A rank zero $p$-converse to a theorem of Gross--Zagier, Kolyvagin and Rubin
Ashay A. Burungale, Ye Tian
https://arxiv.org/abs/2506.03465 https://

A rank zero $p$-converse to a theorem of Gross--Zagier, Kolyvagin and Rubin
Let $E$ be a CM elliptic curve defined over $\mathbb{Q}$ and $p$ a prime. We show that $${\mathrm corank}_{\mathbb{Z}_{p}} {\mathrm Sel}_{p^{\infty}}(E_{/\mathbb{Q}})=0 \implies {\mathrm ord}_{s=1}L(s,E_{/\mathbb{Q}})=0 $$ for the $p^{\infty}$-Selmer group ${\mathrm Sel}_{p^{\infty}}(E_{/\mathbb{Q}})$ and the complex $L$-function $L(s,E_{/\mathbb{Q}})$. Along with Smith's work on the distribution of $2^\infty$-Selmer groups, this leads to the first instance of the even parity Goldfeld conjectur…

Normalised solutions for $p$-Laplacian equations with $L^p$-supercritical growth
Raj Narayan Dhara, Matteo Rizzi
https://arxiv.org/abs/2507.03429 https://

Normalised solutions for $p$-Laplacian equations with $L^p$-supercritical growth
For $N\ge 3$ and $20$ is small enough. The function $V\in L^{N/p}(\mathbb{R}^N)$, which plays the role of potential, is assumed to be non-positive and vanishing at infinity. Moreover, …

RSK correspondence for King tableaux with Berele insertion
Masato Kobayashi, Tomoo Matsumura
https://arxiv.org/abs/2506.06951 https://

RSK correspondence for King tableaux with Berele insertion
We establish a bijective RSK correspondence of type C for King tableaux with Berele insertion as a reformulation of Sundaram's correspondence (1986). For its $Q$-symbol, we make use of semistandard oscillating tableaux (SSOT), a new object which Lee (2025) introduced. Further, we show hidden duality of Cauchy identity through RSK correspondences of type A and C. Finally, we prove that the generating function of SSOT is symmetric by constructing a new sort of Bender-Knuth involution.

This https://arxiv.org/abs/2503.17228 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Mean value of cubic $L$-funcitons with fixed genus
We investigate the mean value of the first moment of primitive cubic $L$-functions over $\mathbb{F}_q(T)$ in the non-Kummer setting. Specifically, we study the sum \begin{equation*} \sum_{\substack{χ primitive\ cubic\\ genus(χ)=g}}L_q(\frac{1}{2}, χ), \end{equation*} where $L_q(s,χ)$ denotes the $L$-function associated with primitive cubic character $χ$. Using double Dirichlet series, we derive an error term of size $q^{(\frac{7}{8}+\varepsilon)g}$.

Expansion of a bivariate symmetric mean in the neighborhood of the first bisector
Bakir Farhi
https://arxiv.org/abs/2506.07601 https://

Expansion of a bivariate symmetric mean in the neighborhood of the first bisector
In this paper, we investigate the behavior of a bivariate mean $M$ near the first bisector by establishing, in several significant cases, an important expansion of $M$ derived from the Taylor expansion of a single-variable function. These expansions are made explicit for a number of classical means. This motivates the introduction of the concept of the characteristic function $Q_M$ of a mean $M$, defined as the second partial derivative of $M$ with respect to its first variable, evaluated along…

Ninth degree analogue of Ramanujan's septic theta function identity
Sun Kim, \"Ors Reb\'ak
https://arxiv.org/abs/2506.01181 https://

Ninth degree analogue of Ramanujan's septic theta function identity
On page 206 in his lost notebook, Ramanujan recorded a seventh degree identity for his theta function $φ(q)$. We give an analogous ninth degree identity. We also provide an application of an entry from his second notebook on a cubic equation and an interpretation with theta functions for some of his trigonometric identities. Lastly, we calculate five examples for $φ(e^{-π\sqrt{n}})$.

The $\mu-$invariant of fine Selmer groups associated to general Drinfeld modules
Hang Chen
https://arxiv.org/abs/2507.02688 https://a…

The $μ-$invariant of fine Selmer groups associated to general Drinfeld modules
Let $F$ be a global function field over the finite field $\mathbb{F}_q$ where $q$ is a prime power and $A$ be the ring of elements in $F$ regular outside $\infty$. Let $ϕ$ be an arbitrary Drinfeld module over $F$ For a fixed non-zero prime ideal $\mathfrak{p}$ of $A$, we show that on the constant $\mathbb{Z}_{\textit{p}}-$extension $\mathfrak{F}$ of $F$, the Pontryagin dual of the fine Selmer group associated to the $\mathfrak{p}-$primary torsion of $ϕ$ over $\mathfrak{F}$ is a finitely gener…

A Selberg-type zero-density result for twisted $\rm GL_2$ $L$-functions and its application
Qingfeng Sun, Hui Wang, Yanxue Yu
https://arxiv.org/abs/2505.23573

A Selberg-type zero-density result for twisted $\rm GL_2$ $L$-functions and its application
Let $f$ be a fixed holomorphic primitive cusp form of even weight $k$, level $r$ and trivial nebentypus $χ_r$. Let $q$ be an odd prime with $(q,r)=1$ and let $χ$ be a primitive Dirichlet character modulus $q$ with $χ\neqχ_r$. In this paper, we prove an unconditional Selberg-type zero-density estimate for the family of twisted $L$-functions $L(s, f \otimes χ)$ in the critical strip. As an application, we establish an asymptotic formula for the even moments of the argument function $S(t, f…

Boundedness of average rank of elliptic curves ordered by the coefficients
Fatemehzahra Janbazi
https://arxiv.org/abs/2506.07089 https://

Boundedness of average rank of elliptic curves ordered by the coefficients
We study the average rank of elliptic curves $E_{A,B} : y^2 = x^3 + Ax + B$ over $\mathbb{Q}$, ordered by the height function $h(E_{A,B}) := \text{max}(|A|, |B|)$. Understanding this average rank requires estimating the number of irreducible integral binary quartic forms under the action of $\mathrm{GL}_2(\mathbb{Z})$, where the invariants $I$ and $J$ are bounded by $X$. A key challenge in this estimation arises from working within regions of the quartic form space that expa…

On the Moments of Exponential Sums over r-Free Polynomials
Ben Doyle
https://arxiv.org/abs/2506.20581 https://arxiv.org/pdf/2506.2058…

On the Moments of Exponential Sums over r-Free Polynomials
Let $\mathbb{F}_q[t]$ denote the ring of polynomials over the finite field $\mathbb{F}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of $k$th moments of exponential sums over $r$-free polynomials in $\mathbb{F}_q[t]$ for all $k>0$. In the supercritical case $k>1+1/r$, we acquire an asymptotic formula using a function field analogue of the Hardy-Littlewood circle method.