Number Theory

Authors and titles for October 2025

[301] arXiv:2510.10272 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Special points on intersections of hypersurfaces Show Chinese title

Title: 高维曲面交集上的特殊点

Claudio Gómez-Gonzáles

Comments: 19 pages. Comments welcome

Subjects: Algebraic Geometry (math.AG) ; Group Theory (math.GR) ; Number Theory (math.NT)

[302] arXiv:2510.10311 (cross-list from math.QA) [cn-pdf, pdf, html, other]

Title: A new criterion for integral modular categorification Show Chinese title

Title: 一种积分模范畴化的新的准则

Jingcheng Dong, Sebastien Palcoux

Comments: 8 pages. Comments are welcome!

Subjects: Quantum Algebra (math.QA) ; Category Theory (math.CT) ; Number Theory (math.NT) ; Representation Theory (math.RT)

[303] arXiv:2510.10330 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Classification of Equivariant Line Bundles on the Drinfeld Upper Half Plane Show Chinese title

Title: 德拉金上半平面的等变线丛分类

Georg Linden

Comments: 41 pages. Comments are welcome

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[304] arXiv:2510.10582 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: $F$-divided bundles on normal $F$-finite schemes Show Chinese title

Title: $F$-分拆包在正常$F$-有限概形上

Adrian Langer, Lei Zhang

Subjects: Algebraic Geometry (math.AG) ; Commutative Algebra (math.AC) ; Algebraic Topology (math.AT) ; Number Theory (math.NT)

[305] arXiv:2510.10834 (cross-list from cs.FL) [cn-pdf, pdf, html, other]

Title: The Tribonacci constant and finite automata Show Chinese title

Title: 三步数常数和有限自动机

Jeffrey Shallit

Subjects: Formal Languages and Automata Theory (cs.FL) ; Discrete Mathematics (cs.DM) ; Number Theory (math.NT)

[306] arXiv:2510.10850 (cross-list from math.DS) [cn-pdf, pdf, html, other]

Title: A topology for Engel expansions: evaluation and digit coding maps Show Chinese title

Title: Engel展开的拓扑：评估和数字编码映射

Min Woong Ahn

Comments: 9 pages

Subjects: Dynamical Systems (math.DS) ; Number Theory (math.NT)

[307] arXiv:2510.11371 (cross-list from math.DS) [cn-pdf, pdf, html, other]

Title: Extreme events and impact statistics for unipotent actions on the space of lattices Show Chinese title

Title: 极端事件和格空间上独异作用的影响统计

Jens Marklof, Andreas Strömbergsson, Shucheng Yu

Comments: 29 pages

Subjects: Dynamical Systems (math.DS) ; Number Theory (math.NT)

[308] arXiv:2510.11477 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Moduli of lattice-polarized K3 surfaces and boundedness of Brauer groups Show Chinese title

Title: 格极化K3曲面的模空间和Brauer群的有界性

Danny Bragg, Emma Brakkee, Anthony Várilly-Alvarado

Comments: Preliminary version. 55 pages

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[309] arXiv:2510.11875 (cross-list from math.AC) [cn-pdf, pdf, html, other]

Title: Commutative algebra inspired by modularity lifting Show Chinese title

Title: 由模提升启发的交换代数

Srikanth B. Iyengar

Comments: This is submitted to the proceedings of the International Congress of Mathematicians 2026. 11 pages. Comments welcome

Subjects: Commutative Algebra (math.AC) ; Number Theory (math.NT)

[310] arXiv:2510.11957 (cross-list from math.DS) [cn-pdf, pdf, html, other]

Title: Furstenberg systems of certain sequences of superpolynomial growth Show Chinese title

Title: 某些超多项式增长序列的Furstenberg系统

Andreu Ferré Moragues, Andreas Koutsogiannis

Comments: 19 pages

Subjects: Dynamical Systems (math.DS) ; Number Theory (math.NT)

[311] arXiv:2510.12883 (cross-list from math.RT) [cn-pdf, pdf, html, other]

Title: Supercuspidal representations: construction, classification, and characters Show Chinese title

Title: 超奇素表示：构造、分类和特征

Jessica Fintzen

Comments: 41 pages, 2 figures, to appear in Proceedings of Symposia in Pure Mathematics

Subjects: Representation Theory (math.RT) ; Number Theory (math.NT)

[312] arXiv:2510.13472 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: The asymptotic estimation for two classes of generalized Fibonacci sub-sequences Show Chinese title

Title: 两类广义斐波那契子序列的渐近估计

Yongkang Wan, Zhonghao Liang, Qunying Liao

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[313] arXiv:2510.13483 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: $L^p$ averages of the discrete Fourier transform and applications Show Chinese title

Title: $L^p$离散傅里叶变换的平均值及应用

Jonathan M. Fraser, Firdavs Rakhmonov

Comments: Expository article, 20 pages, 6 figures

Subjects: Combinatorics (math.CO) ; Classical Analysis and ODEs (math.CA) ; Number Theory (math.NT)

[314] arXiv:2510.13967 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Hilbert property for low-genus families and degree-one del Pezzo surfaces Show Chinese title

Title: 低亏格族的Hilbert性质和一次del Pezzo曲面

Julian Demeio, Sam Streeter, Rosa Winter

Comments: 12 pages, comments welcome

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[315] arXiv:2510.14434 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: The valuation of the discriminant of a hypersurface Show Chinese title

Title: 超曲面判别式的估值

Bjorn Poonen, Michael Stoll

Comments: 14 pages

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[316] arXiv:2510.14473 (cross-list from math.GR) [cn-pdf, pdf, html, other]

Title: Hopf--Galois structures of cyclic type on parallel extensions of prime power degree Show Chinese title

Title: 具有循环类型的Hopf--Galois结构在素数幂次的平行扩张上

Andrew Darlington, Cindy Tsang

Comments: 32 pages

Subjects: Group Theory (math.GR) ; Number Theory (math.NT) ; Rings and Algebras (math.RA)

[317] arXiv:2510.15008 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Evaluating Six Apéry-like Series of Weight $5$ Show Chinese title

Title: 评估六个权重为$5$的阿佩里类似级数

Jorge Antonio González Layja

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[318] arXiv:2510.15108 (cross-list from cs.CR) [cn-pdf, pdf, html, other]

Title: Partitioning $\mathbb{Z}_{sp}$ in finite fields and groups of trees and cycles Show Chinese title

Title: 有限域中$\mathbb{Z}_{sp}$的划分以及树和环的群

Nikolaos Verykios, Christos Gogos

Comments: Preprint version of the manuscript submitted for publication in Fundamenta Informaticae (IOS Press)

Subjects: Cryptography and Security (cs.CR) ; Group Theory (math.GR) ; Number Theory (math.NT)

[319] arXiv:2510.15196 (cross-list from math.AG) [cn-pdf, pdf, other]

Title: Analytic de Rham stacks of Fargues-Fontaine curves Show Chinese title

Title: Fargues-Fontaine曲线的解析德拉姆堆栈

Johannes Anschütz, Guido Bosco, Arthur-César Le Bras, Juan Esteban Rodríguez Camargo, Peter Scholze

Comments: 128 pages

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[320] arXiv:2510.15332 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Blocking sets from a union of plane curves Show Chinese title

Title: 从平面曲线并集中得到的阻塞集

Shamil Asgarli, Dragos Ghioca, Chi Hoi Yip

Comments: 14 pages

Subjects: Algebraic Geometry (math.AG) ; Combinatorics (math.CO) ; Number Theory (math.NT)

[321] arXiv:2510.15743 (cross-list from math.AG) [cn-pdf, pdf, other]

Title: Holomorphic differentials of alternating four covers Show Chinese title

Title: 全纯微分的交替四重覆盖

Frauke M. Bleher, Margarita Bustos Gonzalez

Comments: 38 pages; appendix on indecomposable modules in characteristic 2

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[322] arXiv:2510.16225 (cross-list from math.PR) [cn-pdf, pdf, html, other]

Title: Universality of rational canonical form for random matrices over a finite field Show Chinese title

Title: 有限域上随机矩阵的有理标准形式的普遍性

Jiahe Shen

Comments: 8 pages. Comments welcome!

Subjects: Probability (math.PR) ; Number Theory (math.NT)

[323] arXiv:2510.16277 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Derangements in affine classical groups and Cohen-Lenstra heuristics Show Chinese title

Title: 仿射典型群中的错位排列与Cohen-Lenstra猜想

Jason Fulman, Dennis Stanton

Comments: 8 pages

Subjects: Combinatorics (math.CO) ; Group Theory (math.GR) ; Number Theory (math.NT)

[324] arXiv:2510.16912 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Torsion points of small order on cyclic covers of $\mathbb P^1$. II Show Chinese title

Title: 小阶扭点在$\mathbb P^1$上的循环覆盖。 II

Boris Bekker, Yuri G. Zarhin

Comments: 30 pages

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[325] arXiv:2510.17010 (cross-list from math.KT) [cn-pdf, pdf, other]

Title: Rigidity of the category of localizing motives Show Chinese title

Title: 局部化动机的刚性

Alexander I. Efimov

Comments: 133 pages

Subjects: K-Theory and Homology (math.KT) ; Algebraic Geometry (math.AG) ; Algebraic Topology (math.AT) ; Category Theory (math.CT) ; Number Theory (math.NT)

[326] arXiv:2510.17096 (cross-list from math.DS) [cn-pdf, pdf, html, other]

Title: The Hausdorff dimension of the intersection of $ψ$-well approximable numbers and self-similar sets Show Chinese title

Title: $ψ$佳逼近数的交集的豪斯多夫维数

Suxuan Chen

Comments: 22 pages

Subjects: Dynamical Systems (math.DS) ; Number Theory (math.NT)

[327] arXiv:2510.17112 (cross-list from math.CA) [cn-pdf, pdf, html, other]

Title: Representations of rational numbers and Minkowski dimension Show Chinese title

Title: 有理数的表示和闵可夫斯基维数

Haipeng Chen, Lai Jiang, Yufeng Wu

Subjects: Classical Analysis and ODEs (math.CA) ; Number Theory (math.NT)

[328] arXiv:2510.17744 (cross-list from math.DS) [cn-pdf, pdf, html, other]

Title: Quantitative pyjama Show Chinese title

Title: 定量睡衣

Noah Kravitz, James Leng

Comments: 29 pages, comments welcome!

Subjects: Dynamical Systems (math.DS) ; Combinatorics (math.CO) ; Number Theory (math.NT)

[329] arXiv:2510.18132 (cross-list from math.CA) [cn-pdf, pdf, other]

Title: Beurling Nyman Geometry and Gram Matrix Structure, Ladder Density and Polynomial Decay via Mellin Smoothing Show Chinese title

Title: 贝尔林尼曼几何与格拉姆矩阵结构，通过梅林平滑的阶梯密度和多项式衰减

Hugh Carvill

Comments: 13 pages, 5 figures. Independent research paper on Beurling Nyman geometry and Gram matrix decay. Unconditional analytic results on polynomial decay and block-compressibility (October 2025)

Subjects: Classical Analysis and ODEs (math.CA) ; Number Theory (math.NT)

[330] arXiv:2510.18284 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Effective calculation of local Weil functions via presentations of Cartier divisors Show Chinese title

Title: 通过Cartier除子的表示有效计算局部Weil函数

Nathan Grieve

Comments: Accepted by Houston J. Math

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[331] arXiv:2510.18414 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Upper Bounds for Digitwise Generating Functions of Powers of Two: A Problem and a Matrix Representation Show Chinese title

Title: 两个幂的位数生成函数的上界：一个问题和一个矩阵表示

Hideaki Noda

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT) ; Probability (math.PR)

[332] arXiv:2510.18506 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: A Degree Bound for the c-Boomerang Uniformity Show Chinese title

Title: c-Boomerang 均匀性的度数界

Matthias Johann Steiner

Subjects: Algebraic Geometry (math.AG) ; Cryptography and Security (cs.CR) ; Number Theory (math.NT)

[333] arXiv:2510.18675 (cross-list from math-ph) [cn-pdf, pdf, html, other]

Title: On path integrals for wave functions taking $p$-adic values Show Chinese title

Title: 关于取$p$-adic 值的波函数的路径积分

Su Hu, Min-Soo Kim

Comments: 8 pages

Subjects: Mathematical Physics (math-ph) ; Number Theory (math.NT)

[334] arXiv:2510.18788 (cross-list from math.DS) [cn-pdf, pdf, html, other]

Title: On density analogs of Hindman's finite sums theorem Show Chinese title

Title: 关于希恩曼有限和定理的密度类似物

Felipe Hernández, Ioannis Kousek, Tristán Radić

Comments: Comments are welcome!

Subjects: Dynamical Systems (math.DS) ; Combinatorics (math.CO) ; Number Theory (math.NT)

[335] arXiv:2510.19242 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Congruences modulo powers of $3$ for generalized Frobenius partitions $CΨ_{6,0}$ Show Chinese title

Title: 模$3$幂的广义Frobenius分拆同余关系$CΨ_{6,0}$

Dandan Chen, Siyu Yin

Comments: 8 pages

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[336] arXiv:2510.19355 (cross-list from math.AC) [cn-pdf, pdf, html, other]

Title: Hilbert-Kunz series, F-signature series, and weak p-fractals Show Chinese title

Title: Hilbert-Kunz 系列，F-签名系列，以及弱 p 分形

Alessio Caminata, Francesco Zerman

Comments: to appear in "The Landscape of Commutative Algebra", editors M. Rossi, N.V. Trung, B. Ulrich, and J. Verma, Lecture Note Series of the London Mathematical Society, Cambridge University Press

Subjects: Commutative Algebra (math.AC) ; Number Theory (math.NT)

[337] arXiv:2510.19804 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Forbidden Sidon subsets of perfect difference sets, featuring a human-assisted proof Show Chinese title

Title: 禁止的Sidon子集的完美差集，具有人工辅助证明

Boris Alexeev, Dustin G. Mixon

Comments: 15 pages, 1 figure, 1 ancillary file

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[338] arXiv:2510.19885 (cross-list from cs.CR) [cn-pdf, pdf, html, other]

Title: Analysis and Comparison of Known and Randomly Generated S-boxes for Block Ciphers Show Chinese title

Title: 已知和随机生成的S盒在分组密码中的分析与比较

James Kim

Comments: Master's Dissertation 41 pages

Subjects: Cryptography and Security (cs.CR) ; Number Theory (math.NT)

[339] arXiv:2510.20073 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: An inverse and a stability result for Ruzsa's inequality on triple sumsets Show Chinese title

Title: Ruzsa不等式在三重和集上的逆和稳定性结果

Swaroop Hegde

Comments: 15 pages, 1 figure; added author affiliation info

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[340] arXiv:2510.20509 (cross-list from math.RT) [cn-pdf, pdf, html, other]

Title: Local characters of mod-$\ell$ representations of a $p$-adic reductive group Show Chinese title

Title: 模-$\ell$表示的局部特征的$p$进制约化群

Cheng-Chiang Tsai

Comments: 10 pages. Comments welcome!

Subjects: Representation Theory (math.RT) ; Number Theory (math.NT)

[341] arXiv:2510.20510 (cross-list from math.RT) [cn-pdf, pdf, html, other]

Title: Local character expansion for mod-$\ell$ representations Show Chinese title

Title: 局部特征展开对于模$\ell$表示

Cheng-Chiang Tsai

Comments: The result of this paper is mostly superseded by another paper of myself uploaded on the same day. The method presented here may still be of interest

Subjects: Representation Theory (math.RT) ; Number Theory (math.NT)

[342] arXiv:2510.21562 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Standard conjecture of Hodge type for powers of abelian varieties Show Chinese title

Title: 阿贝尔簇幂的霍奇型标准猜想

Thomas Agugliaro

Comments: 29 pages, comments welcome!

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[343] arXiv:2510.21964 (cross-list from math.DS) [cn-pdf, pdf, html, other]

Title: Density of orbits of horocycle flows at sub-quadratic polynomial times Show Chinese title

Title: 测地流轨道在次二次多项式时间下的密度

Adam Kanigowski, Maksym Radziwiłł

Subjects: Dynamical Systems (math.DS) ; Number Theory (math.NT)

[344] arXiv:2510.22786 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Essential dimension relative to branched covers of degree at most n Show Chinese title

Title: 至多n次分支覆盖的相对本质维数

Benson Farb, Jesse Wolfson

Comments: 9 pages

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[345] arXiv:2510.23022 (cross-list from math.CO) [cn-pdf, pdf, other]

Title: Possible Sizes of Sumsets Show Chinese title

Title: 可能的和集大小

Isaac Rajagopal

Comments: 17 pages, 4 figures

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[346] arXiv:2510.23207 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: The Shimurian BT stack is a gerbe over truncated displays Show Chinese title

Title: Shimurian BT堆栈是截断显示上的gerbe

Eike Lau

Comments: 28 pages

Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT)

[347] arXiv:2510.23233 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Partition analysis and the little Göllnitz identites Show Chinese title

Title: 分拆分析和小Göllnitz恒等式

Runqiao Li

Subjects: Combinatorics (math.CO) ; Number Theory (math.NT)

[348] arXiv:2510.23265 (cross-list from math.RT) [cn-pdf, pdf, other]

Title: Minimal depth $K$-types for wild double covers and Shimura correspondences Show Chinese title

Title: 野生双覆盖和Shimura对应关系的最小深度$K$类型

Edmund Karasiewicz, Shuichiro Takeda

Subjects: Representation Theory (math.RT)

[349] arXiv:2510.23380 (cross-list from math.LO) [cn-pdf, pdf, html, other]

Title: Borel Complexity of the set of vectors normal for a fixed recurrence sequence Show Chinese title

Title: 固定递归序列的正常向量集的Borel复杂性

Hajime Kaneko, Bill Mance

Comments: 23 pages

Subjects: Logic (math.LO) ; Number Theory (math.NT)

[350] arXiv:2510.23543 (cross-list from math.CO) [cn-pdf, pdf, other]

Title: The Erdős-Ginzburg-Ziv constant of rank-two-like $p$-groups Show Chinese title

Title: 二维类似$p$-群的 Erdős-Ginzburg-Ziv 常数

Benjamin Girard, Sofia Zotova

Comments: 18 pages

Subjects: Combinatorics (math.CO) ; Group Theory (math.GR) ; Number Theory (math.NT)