Number Theory

Authors and titles for October 2025

[101] arXiv:2510.10001 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Least zero of pairs of additive cubic equations Show Chinese title

Title: 加性三次方程对的最小零点

Yixiu Xiao, Hongze Li

Comments: 37 pages, 1 figure

Subjects: Number Theory (math.NT)

[102] arXiv:2510.10018 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Galois Action and Localization in Number Fields Show Chinese title

Title: 伽罗瓦作用与数域中的局部化

Jim Coykendall, Jared Kettinger

Comments: 12 pages

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

[103] arXiv:2510.10027 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: $p$-retract Rationality and Norm One Tori Show Chinese title

Title: $p$-收缩 有理性和单位范数环

Kazuki Sato

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

[104] arXiv:2510.10088 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Equivalence criteria for the two--term functional equations for Herglotz--Zagier functions Show Chinese title

Title: 二项式函数方程的等价准则 for Herglotz--Zagier 函数

Sumukha Sathyanarayana, N. Guru Sharan

Comments: 18 pages

Subjects: Number Theory (math.NT)

[105] arXiv:2510.10093 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Mordell--Tornheim zeta function: Kronecker limit type formulas and Special values Show Chinese title

Title: Mordell--Tornheim zeta函数：Kronecker极限类型公式和特殊值

Sumukha Sathyanarayana, N. Guru Sharan

Comments: 25 pages

Subjects: Number Theory (math.NT)

[106] arXiv:2510.10204 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Appell Functions for General Lattices Show Chinese title

Title: Appell函数对于一般格子

Aradhita Chattopadhyaya, Jan Manschot

Comments: 37 pages + appendices

Subjects: Number Theory (math.NT) ; High Energy Physics - Theory (hep-th)

[107] arXiv:2510.10277 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: $L$-functions of elliptic curves in ring class extensions of real quadratic fields via regularized theta liftings Show Chinese title

Title: $L$- 通过正则化θ提升在实二次域的环类扩张中椭圆曲线的函数

Jeanine Van Order

Comments: 43 pp, comments welcome

Subjects: Number Theory (math.NT)

[108] arXiv:2510.10295 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Octic Hilbert 2-class fields of real quadratic fields with discriminant 8p Show Chinese title

Title: 八次实二次域的2类域，判别式为8p

Franz Lemmermeyer

Subjects: Number Theory (math.NT)

[109] arXiv:2510.10303 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Arithmetic Hirzebruch-Zagier divisors and central derivative values of Rankin-Selberg $L$-functions Show Chinese title

Title: 算术Hirzebruch-Zagier除子和Rankin-Selberg$L$函数的中心导数值

Jeanine Van Order

Comments: 83 pp, comments welcome

Subjects: Number Theory (math.NT)

[110] arXiv:2510.10310 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Prime-powered images and irreducible polynomials in dynamical semigroups Show Chinese title

Title: 素数幂图像和动力半群中的不可约多项式

Aristaa Bhardwaj, Adrian Boyer-Paulet, Wade Hindes, Emma Qiu, Alexander Sun

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

[111] arXiv:2510.10403 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Finiteness of Heights in Isogeny Classes of Motives with Semistable Reduction Show Chinese title

Title: 动机在具有半稳定约化的同源类中的高度有限性

Alice Lin

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

[112] arXiv:2510.10418 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A Congruence for Sums of Integer Powers Modulo Products of Distinct Primes Show Chinese title

Title: 一个关于不同素数乘积模的整数幂和的同余式

Shao-Yuan Huang, Hsiu-Yu Wu

Subjects: Number Theory (math.NT)

[113] arXiv:2510.10554 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Kronecker second limit formula for real quadratic fields Show Chinese title

Title: 克罗内克第二极限公式对于实二次域

YoungJu Choie, Rahul Kumar

Comments: Accepted for publication

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

[114] arXiv:2510.10598 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: An alternative proof of the asymptotic formula for the Fourier coefficients of the elliptic modular $j$-function Show Chinese title

Title: 椭圆模函数$j$的傅里叶系数渐近公式的另一种证明

Karin Ikeda

Comments: 20pages, 2tables

Subjects: Number Theory (math.NT)

[115] arXiv:2510.10721 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the distinction between Kloosterman sums and multiplicative functions Show Chinese title

Title: 关于Kloosterman和与乘法函数的区别

Yang Zhang

Subjects: Number Theory (math.NT)

[116] arXiv:2510.10725 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Absolutely Abelian Hilbert Class Fields and $\ell$-torsion conjecture Show Chinese title

Title: 绝对阿贝尔希尔伯特类域和$\ell$-挠猜想

Mahesh Kumar Ram, Prem Prakash Pandey, Nimish Kumar Mahapatra

Subjects: Number Theory (math.NT)

[117] arXiv:2510.10816 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Without real vector spaces all regulators are rational Show Chinese title

Title: 没有实向量空间所有调节器都是有理的

Oliver Braunling

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

[118] arXiv:2510.10853 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: An effective Bombieri-Vinogradov error term for sifting problems Show Chinese title

Title: 筛法问题中有效的Bombieri-Vinogradov误差项

Daniel R. Johnston

Comments: 30 pages

Subjects: Number Theory (math.NT)

[119] arXiv:2510.10855 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Multiplicatively dependent integer vectors on a hyperplane Show Chinese title

Title: 在超平面上的乘法相关的整数向量

Muhammad Afifurrahman, Valentio Iverson, Gian Cordana Sanjaya

Comments: 35 pages, improved bound

Subjects: Number Theory (math.NT)

[120] arXiv:2510.11186 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The Second Moment of $\mathrm{GL}_4 \times \mathrm{GL}_2$ $L$-functions at Special Points Show Chinese title

Title: 二次矩$\mathrm{GL}_4 \times \mathrm{GL}_2$ $L$ -函数在特殊点的值

Zhi Qi, Ruihua Qiao

Comments: 14 pages

Subjects: Number Theory (math.NT)

[121] arXiv:2510.11191 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The Second Moment of $\mathrm{GL}_3 \times \mathrm{GL}_2$ $L$-functions at Special Points Show Chinese title

Title: $\mathrm{GL}_3 \times \mathrm{GL}_2$ $L$ 函数在特殊点的二阶矩

Zhi Qi

Comments: 22 pages

Journal-ref: Math. Ann., 393(1):1429--1457, 2025

Subjects: Number Theory (math.NT)

[122] arXiv:2510.11252 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the Ratat-Goormaghtigh equation and integer points close to the graph of a smooth function Show Chinese title

Title: 关于Ratat-Goormaghtigh方程和光滑函数图像附近的整数点

Tomohiro Yamada

Comments: 12 pages

Subjects: Number Theory (math.NT)

[123] arXiv:2510.11338 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On some conjectural supercongruences involving the sequence $t_n(x)$ Show Chinese title

Title: 关于涉及序列$t_n(x)$的一些猜想型超同余

Hui-Li Han, Chen Wang

Comments: 16 pages

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

[124] arXiv:2510.11511 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the growth of Tate-Shafarevich groups of $p$-supersingular abelian varieties of ${\rm GL}_2$-type over $\mathbb{Z}_p$-extensions of number fields Show Chinese title

Title: 关于数域的$\mathbb{Z}_p$-扩张上$p$-超奇异的${\rm GL}_2$-型阿贝尔簇的Tate-Shafarevich群的增长

Erman Isik, Antonio Lei

Comments: 28 pages

Subjects: Number Theory (math.NT)

[125] arXiv:2510.11559 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Gauss and p-adic numbers Show Chinese title

Title: 高斯和p进数

Franz Lemmermeyer

Subjects: Number Theory (math.NT) ; History and Overview (math.HO)

[126] arXiv:2510.11673 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Integral Matrices of Fixed Rank over Number Fields Show Chinese title

Title: 固定阶数的数域上的积分矩阵

Nihar Gargava, Vlad Serban, Maryna Viazovska, Ilaria Viglino

Comments: Our previous preprint 2402.10305 on this topic is broken into two different parts. This is one of the two parts

Subjects: Number Theory (math.NT) ; Information Theory (cs.IT)

[127] arXiv:2510.11723 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A Normality Conjecture on Rational Base Number Systems Show Chinese title

Title: 有理数基数系统上的正态性猜想

Mélodie Andrieu, Shalom Eliahou, Léo Vivion

Comments: 26 pages, 12 figures

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

[128] arXiv:2510.11753 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: An Effective Method for Solving a Class of Transcendental Diophantine Equations Show Chinese title

Title: 一种求解一类超越不定方程的有效方法

Zeyu Cai

Subjects: Number Theory (math.NT) ; Mathematical Software (cs.MS)

[129] arXiv:2510.11806 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the $v$-adic values of G-functions I Show Chinese title

Title: 关于G-函数的$v$进值 I

Georgios Papas

Comments: Comments welcome

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

[130] arXiv:2510.11814 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the $v$-adic values of G-functions II Show Chinese title

Title: 关于G函数的$v$进值 II

Georgios Papas

Comments: Comments welcome

Subjects: Number Theory (math.NT)

[131] arXiv:2510.11976 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Improved Bounds for the Index Conjecture in Zero-Sum Theory Show Chinese title

Title: 零和理论中指标猜想的改进界

Andrew Pendleton

Journal-ref: Journal of Number Theory 268 (2025) 124-141

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

[132] arXiv:2510.12003 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Noncongruence modular curves as Hurwitz spaces Show Chinese title

Title: 非同余模曲线作为Hurwitz空间

William Y. Chen

Comments: 64 pages, intended for publication in conference proceedings

Subjects: Number Theory (math.NT)

[133] arXiv:2510.12039 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the Number of Small Points for Rational Maps Show Chinese title

Title: 有理映射的小点数量

Jit Wu Yap

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

[134] arXiv:2510.12092 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the generalized Fermat equation $x^{13} + y^{13} = z^n$ Show Chinese title

Title: 关于广义费马方程$x^{13} + y^{13} = z^n$

Alex J. Best, Sander R. Dahmen, Nuno Freitas

Subjects: Number Theory (math.NT)

[135] arXiv:2510.12145 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On Diophantine equations involving intersection of Thabit and Williams numbers base $b$ and some ternary recurrent sequences Show Chinese title

Title: 关于涉及Thabit和Williams数在$b$进制下的交集以及一些三元递归序列的丢番图方程

Bibhu Prasad Tripathy, Asutosh Satapathy, Utkal Keshari Dutta, Bijan Kumar Patel

Subjects: Number Theory (math.NT)

[136] arXiv:2510.12202 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Deformation Theory of Galois Representations and the Taylor--Wiles Method Show Chinese title

Title: 伽罗瓦表示的形变理论与泰勒-威尔斯方法

Ehsan Shahoseini

Comments: This article will be published as a chapter in the CRM proceedings of the AMS Contemporary mathematics, as the proceeding of the second trimester of the year long program on 'Triangle groups, Belyi uniformization and Modularity' organized by Bhaskaracharya Pratishthana, Pune in 2021-22

Subjects: Number Theory (math.NT)

[137] arXiv:2510.12322 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Quantum variance for cubic moment of Hecke--Maass cusp forms and Eisenstein series Show Chinese title

Title: 三次Hecke--Maass尖形式和Eisenstein级数的量子方差

Bingrong Huang, Liangxun Li

Comments: 47 pages, comments welcome!

Subjects: Number Theory (math.NT)

[138] arXiv:2510.12446 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Periods detecting Eisenstein series and sums of $L$-values I Show Chinese title

Title: 周期检测埃森斯坦级数和$L$值的和 I

Weixiao Lu, Guodong Xi

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

[139] arXiv:2510.12496 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On irreducibility of certain low dimensional automorphic Galois representations Show Chinese title

Title: 关于某些低维自守伽罗瓦表示的不可约性

Boyi Dai

Comments: 16 pages

Subjects: Number Theory (math.NT)

[140] arXiv:2510.12533 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On equivariant vector bundles on the Fargues--Fontaine curve over a finite extension Show Chinese title

Title: 关于有限扩张上的法格斯-方丹曲线上的等变向量丛

Rustam Steingart

Comments: Comments welcome

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

[141] arXiv:2510.12625 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Semistable abelian varieties over $\mathbb{Q}$ with bad reduction at 19 only Show Chinese title

Title: 半稳定阿贝尔簇在$\mathbb{Q}$上仅在 19 处有坏约化

Francesco Campagna, Pip Goodman

Comments: 28 pages

Subjects: Number Theory (math.NT)

[142] arXiv:2510.12890 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On $λ$-invariants of congruent modular forms in the anticyclotomic, indefinite setting Show Chinese title

Title: 关于反循环、不定情形中同余模形式的$λ$-不变量

Dac-Nhan-Tam Nguyen

Subjects: Number Theory (math.NT)

[143] arXiv:2510.12893 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Module lattices and their shortest vectors Show Chinese title

Title: 模块格及其最短向量

Nihar Gargava, Vlad Serban, Maryna Viazovska, Ilaria Viglino

Comments: 20 pages. This article is an improved and augmented version of some of the results in arXiv:2402.10305

Subjects: Number Theory (math.NT) ; Information Theory (cs.IT)

[144] arXiv:2510.12956 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Comparing Galois representations in the residually reducible case Show Chinese title

Title: 比较剩余可约情况下的伽罗瓦表示

Nuno Freitas, Ignasi Sánchez-Rodríguez

Comments: 17 pages, the associated code can be found in https://github.com/IgnasiSanchez/ComparingReducibleReps

Subjects: Number Theory (math.NT)

[145] arXiv:2510.12973 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Separable Pseudo-reductive Bands with Applications to Rational Points Show Chinese title

Title: 可分伪约化带及其在有理点中的应用

Azur Đonlagić

Comments: 83 pages

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

[146] arXiv:2510.13076 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Sárközy's theorem for shifted primes with restricted digits Show Chinese title

Title: Sárközy定理对于带有受限数字的移位素数

Alex Burgin

Subjects: Number Theory (math.NT)

[147] arXiv:2510.13172 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Torsion of elliptic curves over $\mathbb{Q}_p$ with good reduction in cyclotomic extensions Show Chinese title

Title: 椭圆曲线在$\mathbb{Q}_p$上的扭结构及其在分圆扩张中的良好约化

Yoshiyasu Ozeki, Manabu Yoshida

Comments: 27pages

Subjects: Number Theory (math.NT)

[148] arXiv:2510.13292 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Counting rational points on elliptic and hyperelliptic curves over function fields Show Chinese title

Title: 在函数域上椭圆曲线和双椭圆曲线上的有理点计数

Jean Gillibert, Emmanuel Hallouin, Aaron Levin

Comments: 23 pages

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

[149] arXiv:2510.13376 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Gauss-Dickson Codes Show Chinese title

Title: 高斯-迪克森码

Shashikant. A. Katre, Vikas S. Jadhav

Comments: 13 Pages

Subjects: Number Theory (math.NT)

[150] arXiv:2510.13469 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Matrices over maximal orders in cyclic division algebras over Q as sums of squares and cubes Show Chinese title

Title: 分圆除代数在Q上的极大序中的矩阵作为平方和立方的和

S.A Katre, Deepa Krishnamurthi

Subjects: Number Theory (math.NT)