Number Theory

Authors and titles for October 2025

[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)