Number Theory

Authors and titles for July 2025

[1] arXiv:2507.00147 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On a conjecture about prime-detecting quasimodular forms Show Chinese title

Title: 关于素数检测拟模形式的一个猜想

Ben Kane, Krishnarjun Krishnamoorthy, Yuk-Kam Lau

Subjects: Number Theory (math.NT)

[2] arXiv:2507.00179 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Averaging quadratically twisted $L$-values and their derivatives Show Chinese title

Title: 二次扭曲$L$值及其导数的平均

Tinghao Huang

Subjects: Number Theory (math.NT)

[3] arXiv:2507.00228 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Distribution of Farey fractions with $k$-free denominators Show Chinese title

Title: 分母为$k$-free 的法里分数的分布

Bittu Chahal, Tapas Chatterjee, Sneha Chaubey

Subjects: Number Theory (math.NT)

[4] arXiv:2507.00325 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On quantum ergodicity for higher dimensional cat maps modulo prime powers Show Chinese title

Title: 关于模素数幂的高维猫映射的量子遍历性

Subham Bhakta, Igor E. Shparlinski

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

[5] arXiv:2507.00326 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Polynomials associated to Lie algebras Show Chinese title

Title: 与李代数相关的多项式

Matías Bruna, Alex Capuñay, Eduardo Friedman

Subjects: Number Theory (math.NT)

[6] arXiv:2507.00404 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Applications of Faà di Bruno's formula to partition traces Show Chinese title

Title: Faà di Bruno公式在划分痕迹中的应用

Toshiki Matsusaka

Comments: 8 pages

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

[7] arXiv:2507.00448 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Counting abelian number fields with restricted ramification type Show Chinese title

Title: 有限分歧类型的阿贝尔数域计数

Julie Tavernier

Comments: 35 pages

Subjects: Number Theory (math.NT)

[8] arXiv:2507.00495 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the Frobenius Problem for Some Generalized Fibonacci Subsequences -- II Show Chinese title

Title: 关于某些广义斐波那契子序列的Frobenius问题——II

Ryan Azim Shaikh, Amitabha Tripathi

Comments: 29 pages, 3 sections, 10 references. arXiv admin note: text overlap with arXiv:2411.04465

Subjects: Number Theory (math.NT)

[9] arXiv:2507.00738 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Murmurations of Modular Forms and $p$-power Coefficients Show Chinese title

Title: 模形式的群集现象与$p$-幂系数

Debanjana Kundu, Katharina Mueller

Comments: Accepted for publication (Math. Proc. Camb. Philos. Soc.). This version has more details than the accepted journal version

Subjects: Number Theory (math.NT)

[10] arXiv:2507.00781 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Permutation polynomials of the form $x+γ\mathrm{Tr}(H(x))$ Show Chinese title

Title: 排列多项式的形式为$x+γ\mathrm{Tr}(H(x))$

Yangcheng Li, Xuan Pang, Pingzhi Yuan, Yuanpeng Zeng

Subjects: Number Theory (math.NT)

[11] arXiv:2507.00860 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Density of algebraic points on products of curves Show Chinese title

Title: 代数点在曲线乘积上的密度

Jennifer Berg, Yu Fu, Evangelia Gazaki, Morena Porzio, James Rawson, Isabel Vogt

Comments: 31 pages. Comments welcome!

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

[12] arXiv:2507.00890 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Une remarque sur l'invariant de Arf Show Chinese title

Title: 关于Arf不变量的一个备注

Alexis Marin

Comments: in French language

Subjects: Number Theory (math.NT)

[13] arXiv:2507.01295 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The length of the repeating decimal Show Chinese title

Title: 循环小数的长度

Siqiong Yao, Akira Toyohara

Comments: 19 pages

Subjects: Number Theory (math.NT)

[14] arXiv:2507.01395 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: More regular formal moduli spaces and arithmetic transfer conjectures: the ramified quadratic case Show Chinese title

Title: 更规则的正式模空间和算术转移猜想：分歧二次情形

Yu Luo, Michael Rapoport, Wei Zhang

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

[15] arXiv:2507.01529 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Some new congruences on biregular overpartitions Show Chinese title

Title: 一些关于双正则过分拆的新同余式

N. K. Meher

Comments: This is the first draft of the paper. Any comments are welcome

Subjects: Number Theory (math.NT)

[16] arXiv:2507.01836 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: $p$-adic moments of $L$-functions Show Chinese title

Title: $p$-进制矩 of$L$-函数

Daniel Kriz, Asbjørn Christian Nordentoft

Comments: arXiv admin note: text overlap with arXiv:2310.20678

Subjects: Number Theory (math.NT)

[17] arXiv:2507.01891 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A weighted divisor problem and exponential sum Show Chinese title

Title: 加权除数问题和指数和

Kritika Aggarwal, Debika Banerjee

Comments: 33 pages

Subjects: Number Theory (math.NT)

[18] arXiv:2507.01898 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The Frobenius number corresponding to the squares of three consecutive Fibonacci numbers: comparison of three algorithmic processes Show Chinese title

Title: 三个连续斐波那契数的平方对应的弗罗贝尼乌斯数：三种算法过程的比较

Aureliano M. Robles-Pérez, José Carlos Rosales

Comments: 18 pages

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

[19] arXiv:2507.02360 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Families of p-adic fields Show Chinese title

Title: p进域的族

Jordi Guàrdia Rúbies, John W. Jones, Kevin Keating, Sebastian Pauli, David P. Roberts, David Roe

Comments: 27 pages

Subjects: Number Theory (math.NT)

[20] arXiv:2507.02522 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Cusp forms of weight 1/2 and pairs of quadratic forms Show Chinese title

Title: 权为1/2的尖点形式和二次型对

András Biró

Comments: A new theorem (Theorem 1.2) is added

Subjects: Number Theory (math.NT)

[21] arXiv:2507.02535 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Monodromy groups and exceptional Hodge classes, II: Sato-Tate groups Show Chinese title

Title: 单值群和例外霍奇类，II：萨托-泰特群

Andrea Gallese, Heidi Goodson, Davide Lombardo

Comments: This is Part II of a revised version of arXiv:2405.20394, which has been split into two parts

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

[22] arXiv:2507.02688 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The $μ-$invariant of fine Selmer groups associated to general Drinfeld modules Show Chinese title

Title: 细Selmer群关于一般Drinfeld模的$μ-$不变量

Hang Chen

Subjects: Number Theory (math.NT)

[23] arXiv:2507.02720 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On Some New Congruences For Biregular Overpartitions Show Chinese title

Title: 关于双正则超分划的一些新同余式

Anakha V

Comments: This is a preliminary version. We would appreciate any feedback or suggestions for improvement from readers

Subjects: Number Theory (math.NT)

[24] arXiv:2507.02739 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Étude statistique du facteur premier médian, 4: somme des inverses Show Chinese title

Title: 中位素因子的统计研究，4：倒数之和

Jonathan Rotgé

Comments: in French language

Subjects: Number Theory (math.NT)

[25] arXiv:2507.02885 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the exceptional set in the $abc$ conjecture Show Chinese title

Title: 关于$abc$猜想中的例外集

Runbo Li

Comments: 15 pages

Subjects: Number Theory (math.NT)

[26] arXiv:2507.03058 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On sums involving powers of harmonic numbers Show Chinese title

Title: 关于调和数幂的和

Lo Ho Tin

Comments: 15 pages, 3 tables

Subjects: Number Theory (math.NT)

[27] arXiv:2507.03413 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Is it true that most sets are Sidon? Show Chinese title

Title: 大多数集合是Sidon集吗？

Paolo Leonetti

Subjects: Number Theory (math.NT) ; General Topology (math.GN)

[28] arXiv:2507.03544 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On uniform Diophantine exponents of lattices Show Chinese title

Title: 关于格的均匀狄利克雷指数

Oleg N. German

Comments: In Russian

Subjects: Number Theory (math.NT)

[29] arXiv:2507.03554 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the weak uniform Diophantine exponent of a real number Show Chinese title

Title: 论实数的弱一致丢番图指数

Oleg N. German

Comments: In Russian

Subjects: Number Theory (math.NT)

[30] arXiv:2507.03727 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Egyptian fractions for few primes Show Chinese title

Title: 埃及分数对于少数素数

Agustina Czenky, Emily McGovern, Julia Plavnik, Eric Rowell, Abigail Watkins

Subjects: Number Theory (math.NT)

[31] arXiv:2507.03784 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Quadratic Chabauty Experiments on Genus 2 Bielliptic Modular Curves in the LMFDB Show Chinese title

Title: 二次Chabauty实验在LMFDB中的2阶双椭圆模曲线

Kate Finnerty

Comments: 17 pages, accepted to LuCaNT 2025 conference proceedings. Version 2 addresses referee comments

Subjects: Number Theory (math.NT)

[32] arXiv:2507.03813 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Existence and Uniqueness Property On a Generalized Ledin-Brousseau Sum Show Chinese title

Title: 广义Ledin-Brousseau和的存在性与唯一性性质

Ivan Hadinata

Comments: There are some revisions in the introduction chapter and references of previous version. One old reference is deleted and two new references are added. Suggestions and corrections are welcome. Thank you

Subjects: Number Theory (math.NT)

[33] arXiv:2507.03824 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Antiquantum $q$-series and mock theta functions Show Chinese title

Title: 反量子$q$系列和模 theta 函数

Amanda Folsom, David Metacarpa

Comments: 14 pages

Subjects: Number Theory (math.NT)

[34] arXiv:2507.04113 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Hecke $L$-series for Sinha modules Show Chinese title

Title: Hecke $L$-级数对于Sinha模块

Erik Davis, Matthew Papanikolas

Comments: 63 pages

Subjects: Number Theory (math.NT)

[35] arXiv:2507.04122 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: The cohomology of certain intermediate strata of Kottwitz varieties Show Chinese title

Title: 某些Kottwitz流形的中间层的上同调

Yachen Liu

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

[36] arXiv:2507.04150 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Selberg's Central Limit Theorem weighted by Linear Statistics of Zeta Zeros Show Chinese title

Title: 塞尔伯格中心极限定理关于黎曼Zeta零点的线性统计权重

Alessandro Fazzari, Maxim Gerspach, Paolo Minelli

Comments: 16 pages

Subjects: Number Theory (math.NT)

[37] arXiv:2507.04231 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Modular resolutions by polyseries Show Chinese title

Title: 模形式的多项式级数分解

Mahdi-Tahar Brahimi

Subjects: Number Theory (math.NT)

[38] arXiv:2507.04402 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On Minimal Excludant over Overpartitions Show Chinese title

Title: 关于过分拆的最小排除数

Judy Ann Donato

Subjects: Number Theory (math.NT)

[39] arXiv:2507.04405 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Twisted Diophantine approximation on manifolds Show Chinese title

Title: 扭曲的丢番图逼近在流形上

Victor Beresnevich, David Simmons, Sanju Velani

Comments: 31 pages

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

[40] arXiv:2507.04521 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Every real number is a sum of two real numbers with diverging partial quotients Show Chinese title

Title: 每个实数都是两个具有发散部分商的实数之和

Dmitry Gayfulin, Erez Nesharim

Comments: 18 pages

Subjects: Number Theory (math.NT)

[41] arXiv:2507.04604 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Class groups of imaginary quadratic points on $X_1(16)$ Show Chinese title

Title: 虚二次点的类群 on $X_1(16)$

Maarten Derickx

Subjects: Number Theory (math.NT)

[42] arXiv:2507.04653 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: $q$-Congruences for Z.-W. Sun's generalized polynomials $w^{(α)}_k(x)$ Show Chinese title

Title: $q$-关于Z.-W. Sun的广义多项式的同余式$w^{(α)}_k(x)$

Lin-Yue Li, Rong-Hua Wang

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

[43] arXiv:2507.04688 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Counting linear congruence systems with a fixed number of solutions Show Chinese title

Title: 具有固定解数的线性同余系统计数

Marcus Nilsson

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

[44] arXiv:2507.04848 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Computing Expansions in Infinitely Many Cantor Real Bases via a Single Transducer Show Chinese title

Title: 通过单个转器在无限多个康托尔实数基中计算展开式

Émilie Charlier, Pierre Popoli, Michel Rigo

Comments: 36 pages, 10 figures. Comments are welcome

Subjects: Number Theory (math.NT) ; Discrete Mathematics (cs.DM) ; Combinatorics (math.CO)

[45] arXiv:2507.04863 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On function fields of curves over higher local fields and their division LFD-algebras Show Chinese title

Title: 关于高阶局部域上曲线的函数域及其分式LFD-代数

Ivan D. Chipchakov

Comments: 11 pages, no figures

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

[46] arXiv:2507.04980 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Quaternionic Kolyvagin systems and Iwasawa theory for Hida families Show Chinese title

Title: 四元数Kolyvagin系统与Hida族的Iwasawa理论

Francesco Zerman

Comments: 34 pages

Subjects: Number Theory (math.NT)

[47] arXiv:2507.05021 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Periods of modular forms and applications to the conjectures of Oda and of Prasanna-Venkatesh Show Chinese title

Title: 模形式的周期及其在奥达猜想和普拉桑纳-文卡特什猜想中的应用

Xavier Guitart, Santiago Molina

Comments: 44 pages

Subjects: Number Theory (math.NT)

[48] arXiv:2507.05374 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: $p$-adic Fourier theory in families Show Chinese title

Title: $p$-adic傅里叶理论在族中

Andrew Graham, Pol van Hoften, Sean Howe

Comments: 80 pages. Comments welcome!

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

[49] arXiv:2507.05693 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Absolute reconstruction of number fields from the Deligne-Ribet monoids Show Chinese title

Title: 数域的绝对重构来自Deligne-Ribet独异群

Takeo Uramoto

Comments: extended the result. 7 pages

Subjects: Number Theory (math.NT)

[50] arXiv:2507.05792 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A full-rank subgroup of Bloch Groups of CM Fields Show Chinese title

Title: CM域的布洛赫群的满秩子群

Wenhuan Huang

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