Number Theory

Authors and titles for October 2025

[1] arXiv:2510.00007 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On Graphical Partitions with Restricted Parts Show Chinese title

Title: 图示分拆中的受限部分

Gilead Levy

Comments: A preliminary version of this work was uploaded to Zenodo: https://doi.org/10.5281/zenodo.17115730. This version includes a revised abstract and introduction

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

[2] arXiv:2510.00012 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A half-shift reflection identity for the digamma function Show Chinese title

Title: 对半移位反射的digamma函数恒等式

Nikita Kalinin

Subjects: Number Theory (math.NT)

[3] arXiv:2510.00016 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Infinitesimal Dilogarithm Satisfies Cluster Identities Show Chinese title

Title: 无穷小双对数满足簇恒等式

Sinan Unver

Subjects: Number Theory (math.NT) ; K-Theory and Homology (math.KT)

[4] arXiv:2510.00020 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Irreducibility and locus of complex roots of polynomials related to Fermat's Last Theorem Show Chinese title

Title: 与费马大定理相关的多项式的不可约性及复根的轨迹

Hayk Karapetyan, Ruben Hambardzumyan

Subjects: Number Theory (math.NT)

[5] arXiv:2510.00130 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Further Applications of Cubic $q$-Binomial Transformations Show Chinese title

Title: 三次$q$-二项式变换的进一步应用

Alexander Berkovich, Aritram Dhar

Comments: 11 pages. Comments are welcome!

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

[6] arXiv:2510.00215 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Continued Fractions and Irrationality Measures for Chowla--Selberg Gamma Quotients Show Chinese title

Title: 连分数和Chowla--Selberg伽马比的无理度量

Henri Cohen, Wadim Zudilin

Comments: 23 pages

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

[7] arXiv:2510.00281 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The Local Companion Points Conjecture Show Chinese title

Title: 局部伴点猜想

Lie Qian

Subjects: Number Theory (math.NT)

[8] arXiv:2510.00295 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Minimal Mahler Measure in Quartic Galois Number Fields Show Chinese title

Title: 四次伽罗瓦数域中的最小梅勒测度

Bishnu Paudel, Kathleen Petersen, Haiyang Wang

Subjects: Number Theory (math.NT)

[9] arXiv:2510.00315 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the Uniqueness of Ein(1) among Linear Combinations of the Euler-Mascheroni and Euler-Gompertz Constants Show Chinese title

Title: 关于Ein(1)在欧拉-马歇罗尼常数和欧拉-贡普茨常数线性组合中的唯一性

Michael R. Powers

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

[10] arXiv:2510.00580 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: The Bruhat-Tits stratification for basic unramified $GU(1,n-1)$ Rapoport-Zink spaces at arbitrary parahoric level Show Chinese title

Title: 布劳特-蒂茨在任意抛物型层次下的基本非分歧$GU(1,n-1)$拉波波特-津克空间的分层结构

Joseph Muller

Comments: 75 pages

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

[11] arXiv:2510.00632 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The local Langlands conjecture Show Chinese title

Title: 局部朗兰兹猜想

Olivier Taïbi

Comments: notes for lectures given at IHES summer school 2022, to appear in Proceedings of Symposia in Pure Mathematics

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

[12] arXiv:2510.00656 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: The Euler characteristic of $\ell$-adic local systems on $\mathcal{A}_n$ Show Chinese title

Title: $\ell$伴随的局部系统在$\mathcal{A}_n$上的欧拉示性数

Olivier Taïbi

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

[13] arXiv:2510.00750 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Elliptic curves and finitely generated Galois groups Show Chinese title

Title: 椭圆曲线和有限生成的伽罗瓦群

Bo-Hae Im, Michael Larsen

Comments: 16 pages

Subjects: Number Theory (math.NT)

[14] arXiv:2510.00775 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Partial Bloch--Kato Selmer groups of $B$-pairs as delta functors Show Chinese title

Title: 部分Bloch--Kato Selmer群关于$B$-对的delta函子

Rustam Steingart

Comments: Comments welcome

Subjects: Number Theory (math.NT) ; K-Theory and Homology (math.KT)

[15] arXiv:2510.00848 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Closed exact categories of modules over generalized adic rings. Part 1: The bounded case Show Chinese title

Title: 闭恰当的模范畴在广义阿廷环上。 第一部分：有界的情形

Francesco Baldassarri

Subjects: Number Theory (math.NT)

[16] arXiv:2510.00870 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On three classes of logarithmic integrals Show Chinese title

Title: 关于三类对数积分

Necdet Batır, Nandan Sai Dasireddy

Subjects: Number Theory (math.NT)

[17] arXiv:2510.00892 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: An Effective Version of the $p$-Curvature Conjecture for Order One Differential Equations Show Chinese title

Title: 一种适用于一阶微分方程的$p$-曲率猜想的有效版本

Florian Fürnsinn, Lucas Pannier

Comments: 30 pages

Subjects: Number Theory (math.NT) ; Symbolic Computation (cs.SC)

[18] arXiv:2510.00926 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the Birch and Swinnerton-Dyer formula modulo squares for certain quadratic twists of elliptic curves Show Chinese title

Title: 关于椭圆曲线某些二次扭转变换的Birch和Swinnerton-Dyer公式的模平方

Alexander J. Barrios, Chung Pang Mok

Comments: 35 pages

Subjects: Number Theory (math.NT)

[19] arXiv:2510.01090 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The Ekedahl-Oort and Newton stratification of the $\mathsf{GU}(3,2)$ Shimura variety Show Chinese title

Title: Ekedahl-Oort 和 Newton 分层的$\mathsf{GU}(3,2)$模形式簇

Emerald Andrews, Deewang Bhamidipati, Maria Fox, Heidi Goodson, Steven R. Groen, Sandra Nair

Comments: 13 pages. This is an expanded version of section 6 of version 1 of arXiv:2405.04464, which we are splitting off into a separate preprint

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

[20] arXiv:2510.01277 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Euler-type Recurrence Relation for Arbitrary Arithmetical Function Show Chinese title

Title: 欧拉型递推关系式对于任意的算术函数

A. David christopher

Journal-ref: INTEGERS Vol. 19 (2019) #A62

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

[21] arXiv:2510.01422 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The $θ$-adics Show Chinese title

Title: 该$θ$-adic

T.M. Gendron, A. Zenteno

Comments: 65 pages

Subjects: Number Theory (math.NT)

[22] arXiv:2510.01440 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Cobham's theorem for the Gaussian integers Show Chinese title

Title: 高斯整数的科布姆定理

Álvaro Bustos-Gajardo, Robbert Fokkink, Reem Yassawi

Comments: 15 pages, 2 figures

Subjects: Number Theory (math.NT) ; Formal Languages and Automata Theory (cs.FL) ; Commutative Algebra (math.AC)

[23] arXiv:2510.01572 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Elementary Proofs and Generalizations of Recent Congruences of Thejitha and Fathima Show Chinese title

Title: 初等证明和最近Thejitha和Fathima同余式的推广

James A. Sellers

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

[24] arXiv:2510.01601 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the Tamagawa number conjecture for modular forms twisted by anticyclotomic Hecke characters Show Chinese title

Title: 关于由反循环Hecke字符扭曲的模形式的Tamagawa数猜想

Takamichi Sano

Comments: 48 pages

Subjects: Number Theory (math.NT)

[25] arXiv:2510.01752 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Odd Spoof Multiperfect Numbers Of Higher Order Show Chinese title

Title: 奇数仿乘完全数的高阶形式

László Tóth

Journal-ref: Comput. Methods Sci. Technol. 31 (1-3), 2025, 63--66

Subjects: Number Theory (math.NT)

[26] arXiv:2510.01781 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Primes of the form $ax+by$ in certain intervals with small solutions Show Chinese title

Title: 形如$ax+by$的素数在某些区间内具有小解

Yuchen Ding, Takao Komatsu, Honghu Liu

Subjects: Number Theory (math.NT)

[27] arXiv:2510.01835 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Mixed moments of Hecke eigenforms and $L$-functions Show Chinese title

Title: Hecke特征形式的混合矩和$L$-函数

Bingrong Huang

Comments: 18 pages. Comments welcome

Subjects: Number Theory (math.NT)

[28] arXiv:2510.01896 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Quantitative growth of multi-recurrence sequences Show Chinese title

Title: 多重递归序列的定量增长

Clemens Fuchs, Armand Noubissie

Subjects: Number Theory (math.NT)

[29] arXiv:2510.02041 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Effective Upper Bound Estimates for $|ζ'(1/2+it)|$ via Exponential Sums Show Chinese title

Title: 通过指数和的有效上界估计$|ζ'(1/2+it)|$

Ting Liu, Jinjin Ma, Binjie Chang, Xinhua Xiong

Comments: v1, 13 pages

Subjects: Number Theory (math.NT)

[30] arXiv:2510.02059 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the $b$-ary expansion of a real number whose irrationality exponent is close to 2 Show Chinese title

Title: 关于实数的$b$进制展开，其无理数指数接近2

Yann Bugeaud, Dong Han Kim

Comments: 14 pages

Subjects: Number Theory (math.NT)

[31] arXiv:2510.02068 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The stable homology of Hurwitz modules and applications Show Chinese title

Title: Hurwitz模的稳定同调及其应用

Aaron Landesman, Ishan Levy

Comments: 91 pages, 12 figures, comments welcome

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

[32] arXiv:2510.02082 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Evaluation of lattice sums via telescoping over topographs Show Chinese title

Title: 通过拓扑图上的望远镜法评估格子和

Nikita Kalinin

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

[33] arXiv:2510.02188 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the behavior of the colored Jones polynomial of the figure-eight knot under modular transformations Show Chinese title

Title: 关于图8 knot 的彩色 Jones 多项式在模变换下的行为

Christoph Aistleitner, Manuel Hauke

Comments: 34 pages, 3 figures

Subjects: Number Theory (math.NT) ; Geometric Topology (math.GT)

[34] arXiv:2510.02273 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A note on Poisson summation for GL(2) Show Chinese title

Title: GL(2)的泊松求和公式注记

Tian An Wong

Comments: 18 pages. Comments welcome

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

[35] arXiv:2510.02309 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Effective Brauer-Siegel theorems for Artin $L$-functions Show Chinese title

Title: 有效Brauer-Siegel定理对于Artin$L$-函数

Peter J. Cho, Robert J. Lemke Oliver, Asif Zaman

Comments: 22 pages

Subjects: Number Theory (math.NT)

[36] arXiv:2510.02699 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the pro-étale cohomology of quotient stacks of Drinfeld spaces Show Chinese title

Title: 关于Drinfeld空间商叠的pro-étale上同调

Zecheng Yi

Comments: 24 pages. Comments welcome!

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

[37] arXiv:2510.02756 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Modularity theorems for abelian surfaces Show Chinese title

Title: 阿贝尔曲面的模性定理

Toby Gee

Comments: Submitted to the 2026 ICM proceedings. 19 pages, comments welcome!

Subjects: Number Theory (math.NT)

[38] arXiv:2510.03068 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Local newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: Uniqueness Show Chinese title

Title: 局部新形式对于泛表示的$p$-进${\rm SO}_{2n+1}$：唯一性

Yao Cheng

Comments: 30 pages

Subjects: Number Theory (math.NT)

[39] arXiv:2510.03373 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Faithfulness and fractal (quasi-)equivalence principles for Perron, Engel, and Pierce expansions Show Chinese title

Title: 忠实性与分形（准）等价原理对于庞特里亚金、恩格尔和皮尔斯展开

Mykola Moroz

Comments: 20 pages, 4 figures

Subjects: Number Theory (math.NT)

[40] arXiv:2510.03476 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Gross's conjecture: the dihedral case Show Chinese title

Title: 格罗斯猜想：二面体情形

Petar Bakić, Aleksander Horawa, Siyan Daniel Li-Huerta, Naomi Sweeting

Comments: 30 pages. Comments welcome!

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

[41] arXiv:2510.03560 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Scattered Behavior Using Modified Cyclotomic Mapping Over Finite Fields Of Odd Characteristic Show Chinese title

Title: 使用有限域奇数特征上的修改型分圆映射的散射行为

Suman Mondal

Comments: 14 pages

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

[42] arXiv:2510.03603 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On Milnor $K$-theory in the imperfect residue case and applications to period-index problems Show Chinese title

Title: 关于不完美剩余域情况下的米尔诺$K$理论及其在周期-指标问题中的应用

Srinivasan Srimathy

Comments: added new results on uniform bounds over semi-global fields

Subjects: Number Theory (math.NT) ; Algebraic Geometry (math.AG) ; K-Theory and Homology (math.KT) ; Rings and Algebras (math.RA)

[43] arXiv:2510.03672 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The Vandermonde Determinant of the Divisors of an Integer Show Chinese title

Title: 整数的除数的范德蒙德行列式

Patrick Letendre

Subjects: Number Theory (math.NT)

[44] arXiv:2510.03828 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Elliptic curves and rational points in arithmetic progression Show Chinese title

Title: 椭圆曲线和有理点的算术级数

Seokhyun Choi

Comments: 21 pages

Subjects: Number Theory (math.NT)

[45] arXiv:2510.04007 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A class of Drinfeld $A$-modules of rank $3$ with surjective Galois representations Show Chinese title

Title: 一类秩为$3$的 Drinfeld$A$模，其伽罗瓦表示是满射的

Narasimha Kumar, Dwipanjana Shit

Subjects: Number Theory (math.NT)

[46] arXiv:2510.04026 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Note on shifted primes with large prime factors Show Chinese title

Title: 关于具有大素因数的移位素数的注记

Yuchen Ding, Zhiwei Wang

Subjects: Number Theory (math.NT)

[47] arXiv:2510.04156 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Arithmetic holonomy bounds and effective Diophantine approximation Show Chinese title

Title: 算术整体性边界和有效的丢番图逼近

Frank Calegari, Vesselin Dimitrov, Yunqing Tang

Comments: This is our submission for the (ICM) Proceedings 2026

Subjects: Number Theory (math.NT)

[48] arXiv:2510.04301 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On quaternionic ordinary families of modular forms and $p$-adic $L$-functions Show Chinese title

Title: 关于四元数普通族的模形式和$p$-adic$L$-函数

Matteo Longo, Paola Magrone, Eduardo Rocha Walchek

Comments: 35 pages

Subjects: Number Theory (math.NT)

[49] arXiv:2510.04306 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Quaternionic families of Heegner points and $p$-adic $L$-functions Show Chinese title

Title: 四元数族的Heegner点和$p$-adic$L$-函数

Matteo Longo, Paola Magrone, Eduardo Rocha Walchek

Comments: 30 pages

Subjects: Number Theory (math.NT)

[50] arXiv:2510.04323 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Reducibility and rational torsion in modular abelian varieties Show Chinese title

Title: 可约性与模阿贝尔簇中的有理扭挠

Amod Agashe, Matthew Winters

Subjects: Number Theory (math.NT) ; Numerical Analysis (math.NA)