Tootfinder

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 …

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…

Endpoint estimates for the fractal circular maximal function and related local smoothing
Sanghyuk Lee, Luz Roncal, Feng Zhang, Shuijiang Zhao
https://arxiv.org/abs/2506.20390

Endpoint estimates for the fractal circular maximal function and related local smoothing
Sharp $L^p$--$L^q$ estimates for the spherical maximal function over dilation sets of fractal dimensions, including the endpoint estimates, were recently proved by Anderson--Hughes--Roos--Seeger. More intricate $L^p$--$L^q$ estimates for the fractal circular maximal function were later established in the sharp range by Roos--Seeger, but the endpoint estimates have been left open, particularly when the fractal dimension of the dilation set lies in $[1/2, 1)$. In this work, we prove these missing…

Determining explicitly the Mordell-Weil group of certain rational elliptic surfaces
Remke Kloosterman
https://arxiv.org/abs/2506.19423 https://

Determining explicitly the Mordell-Weil group of certain rational elliptic surfaces
Let $A,B$ be nonzero rational numbers. Consider the elliptic curve $E_{A,B}/\mathbb{Q}(t)$ with Weierstrass equation $y^2=x^3+At^6+B$. An algorithm to determine $\mathrm{rank } E_{A,B}(\mathbb{Q}(t))$ as a function of $(A,B)$ was presented in a recent paper by Desjardins and Naskrecki. We will give a different and shorter proof for the correctness of that algorithm, using a more geometric approach and discuss for which classes of examples this approach might be useful.

On unbiased estimators for functions of the rate parameter of the exponential distribution
Roberto Vila, Eduardo Yoshio Nakano
https://arxiv.org/abs/2506.20005

On unbiased estimators for functions of the rate parameter of the exponential distribution
In this paper, we explicitly derive unbiased estimators for various functions of the rate parameter of the exponential distribution, including powers of the rate parameter, the $q$th quantile, the $p$th moment, the survival function, the maximum, minimum, probability density function, mean past lifetime, moment generating function, and others. It is also noteworthy that this work corrects a general formula originally proposed by Tate, R. F. (Ann. Math. Statist., 30(2): 341-366, 1959) for constr…

On solutions to Hardy-Sobolev equations on Riemannian manifolds
Guillermo Henry, Jimmy Petean
https://arxiv.org/abs/2506.20089 https://

On solutions to Hardy-Sobolev equations on Riemannian manifolds
Let $(M,g)$ be a closed Riemannian manifold of dimension at least $3$. Let $S$ be the union of the focal submanifolds of an isoparametric function on $(M,g)$. In this article we address the existence of solutions of the Hardy-Sobolev type equation $Δ_g u+K(x)u=\frac{u^{q-1}}{\left(d_{S}(x)\right)^s}$, where $d_{S}(x)$ is the distance from $x$ to $S$ and $q>2$. In particular, we will prove the existence of infinite sign-changing solutions to the equation.

The optimal binding function for (cap, even hole)-free graphs
Ran Chen, Baogang Xu, Yian Xu
https://arxiv.org/abs/2506.19580 https://…

The optimal binding function for (cap, even hole)-free graphs
A {\em hole} is an induced cycle of length at least 4, an {\em even hole} is a hole of even length, and a {\em cap} is a graph obtained from a hole by adding an additional vertex which is adjacent exactly to two adjacent vertices of the hole. A graph $G$ obtained from a graph $H$ by blowing up all the vertices into cliques is said to be a clique blowup of $H$. Let $p, q$ be two positive integers with $p>2q$, let $F$ be a triangle-free graph, and let $G'$ be a clique blowup of $F$ with $ω(G')\l…

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.

Distribution of codewords on the faces of a hypercube and new combinatorial identities
Jamolidin K. Abdurakhmanov
https://arxiv.org/abs/2506.18494 https://…

Distribution of codewords on the faces of a hypercube and new combinatorial identities
We present a novel framework for studying combinatorial identities through the geometric lens of subset distributions in q-valued cubes. By analyzing how elements of arbitrary subsets are distributed among the faces of the cube E_q^n, we discover new combinatorial identities with geometric significance. We prove that for any subset A contained in E_2^n, the rank function satisfies refined bounds that lead to exact computations for small cardinalities. Specifically, we show that for odd cardinal…

Coupled Entropy: A Goldilocks Generalization?
Kenric P. Nelson
https://arxiv.org/abs/2506.17229 https://arxiv.org/pdf/2506.17229

Coupled Entropy: A Goldilocks Generalization?
Nonextensive Statistical Mechanics (NSM) has developed into a powerful toolset for modeling and analyzing complex systems. Despite its many successes, a puzzle arose early in its development. The constraints on the Tsallis entropy are in the form of an escort distribution with elements proportional to $p_i^q$, but this same factor within the Tsallis entropy function is not normalized. This led to consideration of the Normalized Tsallis Entropy (NTE); however, the normalization proved to make th…

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…

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case
Anna Skorobogatova, Luca Spolaor, Salvatore Stuvard
https://arxiv.org/abs/2506.17813

Structure of two-dimensional mod$(q)$ area-minimizing currents near flat singularities: the codimension one case
We obtain a fine structural result for two-dimensional mod$(q)$ area-minimizing currents of codimension one, close to flat singularities. Precisely, we show that, locally around any such singularity, the current is a $C^{1,α}$-perturbation of the graph of a radially homogeneous special multiple-valued function that arises from a superposition of homogeneous harmonic polynomials. Additionally, as a preliminary step towards an analogous result in arbitrary codimension, we prove in general that t…

A Remark on a Kind of Oscillatory Singular Integrals with Nonstarnd Kernel and Fewnomials Phases
Shen Jiawei
https://arxiv.org/abs/2506.17617 https://

A Remark on a Kind of Oscillatory Singular Integrals with Nonstarnd Kernel and Fewnomials Phases
In the paper, we study a kind of Oscillatory singular integral operator $T_{Q,A}$ with nonstandard Kernel defined by \[T_{Q,A} f(x)=\text { p.v. } \int_{\mathbb{R}^{n}} f(y) \frac{Ω(x-y)}{|x-y|^{n}}(A(x)-A(y)-\nabla A(x-y) e^{i Q(|x-y|)} d y, \] where $Q(t)$ is a real polynomial on $\mathbb{R}$, and $Ω$ is s a homogenous function of degree zero on $\mathbb{R}$ and satisfy satisfies the vanishing moment condition. Under the condition that $Ω\in Llog^2(\mathbb{R}^{n}),$ we …

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…

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 $a_{1} a_{2} \cdots a_{n}$ …

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 $x\in \mathbb{R}$, …

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…

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_…

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…

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 …

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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…

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 …

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

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 $K$.

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…

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…

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…

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(…

This https://arxiv.org/abs/2502.15465 has been replaced.
link: https://scholar.google.com/scholar?q=a

Revisiting gluon density from the BK equation with kinematical constraint and large x terms
We perform analysis of the small x non-linear evolution equation formulated in momentum space supplemented by higher order terms. The equation is defined in wide range of transverse momentum and longitudinal momentum fraction extending previous studies performed in \cite{Kutak:2003bd,Kutak:2004ym}. The linear part of the equation is motivated by the renormalization group improved small x approach which accounts for resummation of higher orders, and includes collinear splitting function and kine…

This https://arxiv.org/abs/2407.01828 has been replaced.
link: https://scholar.google.com/scholar?q=a

Folding and Metric Entropies for Extended Shifts
In this paper we calculate the metric and folding entropies for a family of non-invertible symbolic dynamical systems $(Σ_{m_-,m_+}, σ_ϕ)$ which generalizes the standard bilateral Bernoulli shifts. The space $Σ_{m_-,m_+}$ consists of symbolic sequences over two distinct finite alphabets, with dynamics governed by a shift map $σ_ϕ$ incorporating a non-invertible function $ϕ$ that maps one of the alphabets to the other one. These systems are, for instance, particularly useful for encoding …

Learning to Charge More: A Theoretical Study of Collusion by Q-Learning Agents
Cristian Chica, Yinglong Guo, Gilad Lerman
https://arxiv.org/abs/2505.22909 …

Learning to Charge More: A Theoretical Study of Collusion by Q-Learning Agents
There is growing experimental evidence that $Q$-learning agents may learn to charge supracompetitive prices. We provide the first theoretical explanation for this behavior in infinite repeated games. Firms update their pricing policies based solely on observed profits, without computing equilibrium strategies. We show that when the game admits both a one-stage Nash equilibrium price and a collusive-enabling price, and when the $Q$-function satisfies certain inequalities at the end of experiment…

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/2506.00971 has been replaced.
link: https://scholar.google.com/scholar?q=a

Resonant Tunneling in Tri-layer 2H-MoTe2 grown by Molecular Beam Epitaxy Coupled with layered WSe2 carrier Reservoir
Here, we report a prominent quantum oscillation in the conductance of 2H-MoTe2 based resonant tunneling structure. In this work, a n-WSe2/HfO2/i-MoTe2/HfO2/Au resonant tunneling device (RTD) with a symmetric and asymmetric double barrier has been fabricated using Molecular Beam Epitaxy (MBE) grown 2H-MoTe2 and Chemical Vapor Deposition (CVD) grown 2H-WSe2 along with theoretical modeling by adopting non-equilibrium Green function (NEGF) formalism. The impact of MoTe2-quantum well widths equal, a…

This https://arxiv.org/abs/2007.13121 has been replaced.
link: https://scholar.google.com/scholar?q=a

Efficient Approximation Schemes for Stochastic Probing and Selection-Stopping Problems
In this paper, we propose a general framework to design {efficient} polynomial time approximation schemes (EPTAS) for fundamental stochastic combinatorial optimization problems. Given an error parameter $ε>0$, such algorithmic schemes attain a $(1-ε)$-approximation in $t(ε)\cdot poly(|{\cal I}|)$ time, where $t(\cdot)$ is a function that depends only on $ε$ and $|{\cal I}|$ denotes the input length. Technically speaking, our approach relies on presenting tailor-made redu…

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/2208.09407 has been replaced.
link: https://scholar.google.com/scholar?q=a

Learning in Stackelberg Games with Non-myopic Agents
We study Stackelberg games where a principal repeatedly interacts with a non-myopic long-lived agent, without knowing the agent's payoff function. Although learning in Stackelberg games is well-understood when the agent is myopic, dealing with non-myopic agents poses additional complications. In particular, non-myopic agents may strategize and select actions that are inferior in the present in order to mislead the principal's learning algorithm and obtain better outcomes in the future. We pro…

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}

This https://arxiv.org/abs/2207.01666 has been replaced.
link: https://scholar.google.com/scholar?q=a

Cutoff stability of multivariate geometric Brownian motion
This article establishes cutoff convergence or abrupt convergence of three statistical quantities for multivariate (Hurwitz) stable geometric Brownian motion: the autocorrelation function, the Wasserstein distance between the current state and its degenerate limiting measure, and, finally, anti-concentration probabilities, which yield a fine-tuned trade-off between almost sure rates and the respective integrability of the random modulus of convergence using a quantitative Borel--Cantelli Lemma.…

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…

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…

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…

Distributed Neural Policy Gradient Algorithm for Global Convergence of Networked Multi-Agent Reinforcement Learning
Pengcheng Dai, Yuanqiu Mo, Wenwu Yu, Wei Ren
https://arxiv.org/abs/2505.24113

Distributed Neural Policy Gradient Algorithm for Global Convergence of Networked Multi-Agent Reinforcement Learning
This paper studies the networked multi-agent reinforcement learning (NMARL) problem, where the objective of agents is to collaboratively maximize the discounted average cumulative rewards. Different from the existing methods that suffer from poor expression due to linear function approximation, we propose a distributed neural policy gradient algorithm that features two innovatively designed neural networks, specifically for the approximate Q-functions and policy functions of agents. This distri…

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…

This https://arxiv.org/abs/2204.08031 has been replaced.
link: https://scholar.google.com/scholar?q=a

Limit theorems of Chatterjee's rank correlation
Establishing the limiting distribution of Chatterjee's rank correlation for a general, possibly non-independent, pair of random variables has been eagerly awaited by many. This paper shows that (a) Chatterjee's rank correlation is asymptotically normal as long as one variable is not a measurable function of the other, (b) the corresponding asymptotic variance is uniformly bounded by 36, and (c) a consistent variance estimator exists. Similar results also hold for Azadkia-Chatterjee's graph-base…

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…

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.

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…

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.

This https://arxiv.org/abs/2009.11945 has been replaced.
link: https://scholar.google.com/scholar?q=a

Some application of Grunsky coefficients in the theory of univalent functions
Let function $f$ be normalized, analytic and univalent in the unit disk ${\mathbb D}=\{z:|z|<1\}$ and $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$. Using a method based on Grusky coefficients we study several problems over that class of univalent functions: upper bounds of the special case of the generalised Zalcman conjecture $|a_2a_3-a_4|$, of the third logarithmic coefficient, and of the second Hankel determinant for the logarithmic coefficients.

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. …

This https://arxiv.org/abs/2408.08294 has been replaced.
link: https://scholar.google.com/scholar?q=a

eGAD! double descent is explained by Generalized Aliasing Decomposition
A central problem in data science is to use potentially noisy samples of an unknown function to predict values for unseen inputs. In classical statistics, predictive error is understood as a trade-off between the bias and the variance that balances model simplicity with its ability to fit complex functions. However, over-parameterized models exhibit counterintuitive behaviors, such as "double descent" in which models of increasing complexity exhibit decreasing generalization error. Others may e…

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 $q^{(\frac{7}{8}+\varepsilon)g}$.

Discrete and Continuous Muttalib--Borodin process: Large deviations and Riemann--Hilbert analysis
Jonathan Husson, Guido Mazzuca, Alessandra Occelli
https://arxiv.org/abs/2505.23164

Discrete and Continuous Muttalib--Borodin process: Large deviations and Riemann--Hilbert analysis
In this paper, we study the asymptotic behaviour of plane partitions distributed according to a weighted $q^{Volume}$ Muttalib--Borodin ensemble. Specifically, we establish a Large Deviation principle for the discrete Muttalib--Borodin process, characterising the rate function. Furthermore, through Riemann--Hilbert analysis, we give an explicit expression for the asymptotic shape of the partition.

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 $φ(e^{-π\sqrt{n}})$.

Sequences of LCD AG codes and LCP of AG Codes attaining the Tsfasman-Vladut-Zink bound
Adler Marques, Luciane Quoos
https://arxiv.org/abs/2505.23937 https:…

Sequences of LCD AG codes and LCP of AG Codes attaining the Tsfasman-Vladut-Zink bound
Since Massey introduced linear complementary dual (LCD) codes in 1992 and Bhasin et al. later formalized linear complementary pairs (LCPs) of codes - structures with important cryptographic applications - these code families have attracted significant interest. We construct infinite sequences $(C_i)_{i \geq 1}$ of LCD codes and of LCPs $(C', D')_{i \geq 1}$ over $\mathbb{F}_{q^2}$ obtained from the Garcia-Stichtenoth tower of function fields, where we describe suitable non-special divisors of s…

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…

Embedding theorems for Bergman-Zygmund spaces induced by doubling weights
Atte Pennanen
https://arxiv.org/abs/2505.23211 https://arxi…

Embedding theorems for Bergman-Zygmund spaces induced by doubling weights
Let $0

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…

This https://arxiv.org/abs/2212.03159 has been replaced.
link: https://scholar.google.com/scholar?q=a

Optimal growth of upper frequently hypercyclic functions for some weighted Taylor shifts
We are interested in the optimal growth in terms of $L^p$-averages of hypercyclic and $\mathcal{U}$-frequently hypercyclic functions for some weighted Taylor shift operators acting on the space of analytic function on the unit disc. We unify the results obtained by considering intermediate notions of upper frequent hypercyclicity between the $\mathcal{U}$-frequent hypercyclicity and the hypercyclicity.

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…

This https://arxiv.org/abs/2212.00636 has been replaced.
link: https://scholar.google.com/scholar?q=a

Newman's conjecture for the partition function modulo integers with at least two distinct prime divisors
Let $M$ be a positive integer and $p(n)$ be the number of partitions of a positive integer $n$. Newman's Conjecture asserts that for each integer $r$, there are infinitely many positive integers $n$ such that \[ p(n)\equiv r \pmod{M}. \] For a positive integer $d$, let $B_{d}$ be the set of positive integers $M$ such that the number of prime divisors of $M$ is $d$. In this paper, we prove that for each positive integer $d$, the density of the set of positive integers $M$ for which Newman's Conj…