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Coxeter matrices and homological quadratic forms of $\boldsymbol{n}$-hereditary algebras
Raziyeh Diyanatnezhad, Alireza Nasr-Isfahani
https://arxiv.org/abs/2506.13136

Coxeter matrices and homological quadratic forms of $\boldsymbol{n}$-hereditary algebras
We study the Coxeter matrices and the homological quadratic forms of $n$-hereditary algebras within the framework of higher dimensional Auslander--Reiten theory. Let $Λ$ be a finite dimensional $n$-hereditary algebra with the Coxeter matrix $Φ$ and the homological quadratic form $χ$. We prove that if $Λ$ is $n$-representation finite, then there exists a positive integer $d$ such that $Φ^d=1$. In the case $n$ is an odd number, we show that if there exists a positive integer $d$ such that $Î…

Positive Sharing and Abstract Machines
Beniamino Accattoli, Claudio Sacerdoti Coen, Jui-Hsuan Wu
https://arxiv.org/abs/2506.14131 https://

Positive Sharing and Abstract Machines
Wu's positive $λ$-calculus is a recent call-by-value $λ$-calculus with sharing coming from Miller and Wu's study of the proof-theoretical concept of focalization. Accattoli and Wu showed that it simplifies a technical aspect of the study of sharing; namely it rules out the recurrent issue of renaming chains, that often causes a quadratic time slowdown. In this paper, we define the natural abstract machine for the positive $λ$-calculus and show that it suffers from an inefficiency: the quad…

Character sums to prime power moduli evaluated at binary quadratic forms
Stephan Baier, Aishik Chattopadhyay
https://arxiv.org/abs/2508.11231 https://arxiv…

Character sums to prime power moduli evaluated at binary quadratic forms
We establish estimates for short character sums to prime power moduli evaluated at binary quadratic forms. This complements estimates established by Heath-Brown for such character sums to squarefree moduli. To this end, we use tools from the $p$-adic theory of exponential sums, as initiated by Milićević.

On quadratic persistence and Pythagoras numbers of totally real projective varieties
Jong In Han, Jaewoo Jung, Euisung Park
https://arxiv.org/abs/2506.13247

On quadratic persistence and Pythagoras numbers of totally real projective varieties
In this paper, we study the relationship between quadratic persistence and the Pythagoras number of totally real projective varieties. Building upon the foundational work of Blekherman et al. in arXiv:1902.02754, we extend their characterizations of arithmetically Cohen-Macaulay varieties with next-to-maximal quadratic persistence to arbitrary case. Our main result classifies totally real non-aCM varieties of codimension $c$ and degree $d$ that exhibit next-to-maximal quadratic persistence in t…

Important Bit Prefix M-ary Quadrature Amplitude Modulation for Semantic Communications
Haonan Lu, Rui Meng, Xiaodong Xu, Yiming Liu, Ping Zhang, Dusit Niyato
https://arxiv.org/abs/2508.11351

Important Bit Prefix M-ary Quadrature Amplitude Modulation for Semantic Communications
M-ary Quadrature Amplitude Modulation (MQAM) is a commonly used channel modulation technology in wireless communication systems. To achieve dedicated channel modulation for semantic communication (SemCom), we propose an Important-Bit-Prefixed MQAM (IBP-MQAM) scheme and derive its approximate expression of important symbol error rate (ISER) and unimportant symbol error rate (USER). By extracting and quantifying text semantics using Latent Dirichlet Allocation (LDA), we verify that IBP-MQAM achie…

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A High-Order Quadrature Method for Implicitly Defined Hypersurfaces and Regions
Zibo Zhao
https://arxiv.org/abs/2506.13078 https://ar…

A High-Order Quadrature Method for Implicitly Defined Hypersurfaces and Regions
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided into small tetrahedrons, and by employing the change of variables formula, the approach yields an algorithm requiring only one-dimensional root finding and standard Gaussian quadrature. The resulting quadrature scheme guarantees strictly positive weights and …

On a Variant of Pillai's problem involving convergent denominators of quadratic irrationals
Mohit Mittal
https://arxiv.org/abs/2508.11243 https://arxiv…

On a Variant of Pillai's problem involving convergent denominators of quadratic irrationals
Let $(q_{α, n})_{n \geq 0}$ be the sequence of convergent denominators to the simple continued fraction expansion of $α$. For certain specific choices of $α$, this sequence is a Lehmer sequence. In this paper, we show that there are only finitely many integers $c$ such that the equation $q_{α, n} - q_{β, m} = c$ has at least two distinct solutions $(n,m)$, where $α,β$ are quadratic irrationals with $\mathbb{Q}(α)\neq \mathbb{Q}(β)$. In specific instances, we solve the equation $q_{α, …

An explicit decomposition of higher Deligne-Lsuztig representations
Ben Liu, Sian Nie
https://arxiv.org/abs/2506.12918 https://arxiv.…

An explicit decomposition of higher Deligne-Lsuztig representations
In a previous paper, the second named author obtains a decomposition of an elliptic higher Deligne-Lusztig representation into irreducible summands, which are built in the same way as Yu types using a geometric analog $κ'$ of the Weil-Heisenberg representation $κ$. In this note, we show that $κ'$ and $κ$ differs by a character $χ$. Moreover, under a mild condition on the cardinality $q$ of the residue field (for instance $q > 3$), we show that $χ$ equals the quadratic character constructe…

A simplified algorithmic realization of Galois actions on special values of modular functions
Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon
https://arxiv.org/abs/2506.14139

A simplified algorithmic realization of Galois actions on special values of modular functions
We propose an explicit and practical algorithm for computing Galois conjugates and irreducible polynomials for special values of modular functions evaluated at CM points associated with imaginary quadratic orders. Our approach builds upon the theory of extended form class groups developed by Jung et al., offering a refinement of earlier methods by Stevenhagen and Cho, respectively.