Number Theory

Authors and titles for June 2024

[101] arXiv:2406.09081 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Multifractal analysis of the growth rate of digits in Schneider's $p$-adic continued fraction dynamical system Show Chinese title

Title: 分形分析施耐德的$p$-进制连分数动力系统的数字增长速率

Kunkun Song, Wanlou Wu, Yueli Yu, Sainan Zeng

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

[102] arXiv:2406.09107 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Square roots and lattices Show Chinese title

Title: 平方根和格

Jens Marklof

Comments: 10 pages; 4 figures; to appear in L'Enseignement Math\'ematique

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

[103] arXiv:2406.09114 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Polynomial p-adic Low-Discrepancy Sequences Show Chinese title

Title: 多项式 p 进低差异序列

Christian Weiß

Subjects: Number Theory (math.NT)

[104] arXiv:2406.09243 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On averages of completely multiplicative functions over co-prime integer pairs Show Chinese title

Title: 关于完全乘性函数在互质整数对上的平均值

Biao Wang

Comments: 12 pages

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

[105] arXiv:2406.09256 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Integral solutions to systems of diagonal equations Show Chinese title

Title: 对角方程组的积分解

Nick Rome, Shuntaro Yamagishi

Comments: Significant updates to fill in gaps and bring results more in line with the state of the art in Waring's problem

Subjects: Number Theory (math.NT)

[106] arXiv:2406.09360 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On Arratia's coupling and the Dirichlet law for the factors of a random integer Show Chinese title

Title: 关于阿拉蒂亚耦合和随机整数因子的狄利克雷定律

Tony Haddad, Dimitris Koukoulopoulos

Comments: 37 pages, minor corrections. Final version, published in Journal de l'\'Ecole polytechnique -- Math\'ematiques

Journal-ref: Journal de l'\'Ecole polytechnique -- Math\'ematiques, Tome 12 (2025), pp. 1565-1604

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

[107] arXiv:2406.09364 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the existence of magic squares of powers Show Chinese title

Title: 关于幂幻方的存在性

Nick Rome, Shuntaro Yamagishi

Comments: Updated version features revised algorithm making computer search unnecessary as well as proper credit for the work of Flores

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

[108] arXiv:2406.09532 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the congruence properties and growth rate of a recursively defined sequence Show Chinese title

Title: 关于一个递归定义序列的同余性质和增长率

Wouter van Doorn

Comments: 18 pages

Subjects: Number Theory (math.NT)

[109] arXiv:2406.09633 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: An effective Deligne's equidistribution theorem Show Chinese title

Title: 有效的德尔涅等分布定理

Lei Fu, Yuk-Kam Lau, Ping Xi

Comments: Improve the estimates in the previous version

Subjects: Number Theory (math.NT)

[110] arXiv:2406.09778 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Small Solutions of generic ternary quadratic congruences Show Chinese title

Title: 关于一般三元二次同余式的微小解

Stephan Baier, Aishik Chattopadhyay

Comments: 10 pages

Subjects: Number Theory (math.NT)

[111] arXiv:2406.09796 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Trivial zeros of Riemann auxiliary function Show Chinese title

Title: 黎曼辅助函数的平凡零点

Juan Arias de Reyna

Comments: 5 pages

Subjects: Number Theory (math.NT)

[112] arXiv:2406.10014 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Powered numbers in short intervals II Show Chinese title

Title: 短区间内的幂数 II

Tsz Ho Chan

Comments: 7 pages

Subjects: Number Theory (math.NT)

[113] arXiv:2406.10106 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Equidistribution of Kloosterman sums over function fields Show Chinese title

Title: 函数域上Kloosterman和的等分布

Lei Fu, Yuk-Kam Lau, Wen-Ching Winnie Li, Ping Xi

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

[114] arXiv:2406.10385 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Finite monodromy of some two-parameter families of exponential sums Show Chinese title

Title: 某些双参数指数和族的有限单值性

Francisco García-Cortés, Antonio Rojas-León

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

[115] arXiv:2406.10404 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Solvability of $\binom{2k}{k} = \binom{2a}{a} \binom{x+2b}{b}$ Show Chinese title

Title: $\binom{2k}{k} = \binom{2a}{a} \binom{x+2b}{b}$的可解性

Meaghan Allen

Subjects: Number Theory (math.NT)

[116] arXiv:2406.10414 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the Field Isomorphism Problem for the Family of Simplest Quartic Fields Show Chinese title

Title: 关于最简四次域族的域同构问题

David L. Pincus, Lawrence C. Washington

Comments: 10 pages

Subjects: Number Theory (math.NT)

[117] arXiv:2406.10440 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Extending class group action attacks via sesquilinear pairings Show Chinese title

Title: 通过共轭双线性对扩展类群作用攻击

Joseph Macula, Katherine E. Stange

Comments: 25 pages

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

[118] arXiv:2406.10604 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Some remarks on the order structures of multi-polylogarithms Show Chinese title

Title: 关于多对数函数的序结构的一些备注

Ken Kamano

Comments: 11 pages

Subjects: Number Theory (math.NT)

[119] arXiv:2406.10609 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Orthogonal involutions over fields with I^3=0 Show Chinese title

Title: 域上满足I³=0的正交对合

Karim Johannes Becher, Fatma Kader Bingöl

Comments: 23 pages

Journal-ref: J. Pure Appl. Algebra 229 (2025), no. 6, Paper No. 107979

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

[120] arXiv:2406.10820 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Approximation measures for shifted logarithms of algebraic numbers via effective Poincare-Perron Show Chinese title

Title: 通过有效庞加莱-佩龙方法对代数数的位移对数的近似度量

Noriko Hirata-Kohno, Ryuji Muroi, Yusuke Washio

Comments: 12 pages, minor revision

Subjects: Number Theory (math.NT)

[121] arXiv:2406.11279 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Zeros of $\mathop{\mathcal R}(s)$ on the fourth quadrant Show Chinese title

Title: $\mathop{\mathcal R}(s)$在第四象限的零点

Juan Arias de Reyna

Comments: 14 pages, 3 figures

Subjects: Number Theory (math.NT)

[122] arXiv:2406.11302 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Vanishing of Poincaré series for congruence subgroups Show Chinese title

Title: Poincaré 系列在同余子群中的消失

Noam Kimmel

Subjects: Number Theory (math.NT)

[123] arXiv:2406.11479 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: A proof of Sugawara's conjecture on Hasse-Weber ray class invariants Show Chinese title

Title: Sugawara关于Hasse-Weber射类不变量的猜想的证明

Patrick Morton

Comments: 75 pages; an additional case of the conjecture has now been included in Section 6.2

Subjects: Number Theory (math.NT)

[124] arXiv:2406.11529 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Fourier transform in cyclic groups Show Chinese title

Title: 循环群中的傅里叶变换

Yves Benoist (CNRS)

Comments: This version 2 contains a new chapter "Unimodular C-functions for safe prime" that deal with H. Cohn's question for safe primes

Subjects: Number Theory (math.NT)

[125] arXiv:2406.12010 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Criteria for the integrality of $n$th roots of power series Show Chinese title

Title: 幂级数的$n$次根的整性条件

John Pomerat, Armin Straub

Comments: 11 pages

Subjects: Number Theory (math.NT)

[126] arXiv:2406.12152 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the Stieltjes Approximation Error to Logarithmic Integral Show Chinese title

Title: 关于对数积分的Stieltjes逼近误差

Jonatan Gomez

Comments: 21 ppages, 2 Figures (each with 3 subfigures)

Subjects: Number Theory (math.NT)

[127] arXiv:2406.12283 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A generalization of the Titchmarsh divisor problem Show Chinese title

Title: 蒂奇马什除数问题的推广

Biao Wang

Comments: 7 pages

Subjects: Number Theory (math.NT)

[128] arXiv:2406.12290 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Improving Behrend's construction: Sets without arithmetic progressions in integers and over finite fields Show Chinese title

Title: 改进Behrend的构造：整数和有限域中没有等差数列的集合

Christian Elsholtz, Zach Hunter, Laura Proske, Lisa Sauermann

Comments: (15 pages). This manuscript replaces the two manuscripts arXiv:2401.12802 and arXiv:2401.16106

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

[129] arXiv:2406.12332 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Congruences for sums of MacMahon's $q$-Catalan polynomials Show Chinese title

Title: MacMahon的$q$-卡特兰多项式求和的同余关系

Tewodros Amdeberhan, Roberto Tauraso

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

[130] arXiv:2406.12344 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Infinite Product of the Riemann auxiliary function Show Chinese title

Title: 黎曼辅助函数的无穷乘积

Juan Arias de Reyna

Comments: 12 pages

Subjects: Number Theory (math.NT)

[131] arXiv:2406.12351 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Hida family of theta lift from U(1) to definite U(2) Show Chinese title

Title: Hida 族的θ提升从U(1)到确定的U(2)

Yu-Sheng Lee

Comments: Slight changes in the statements and notation, with additional clarifications added in the final chapter

Subjects: Number Theory (math.NT)

[132] arXiv:2406.12455 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the structure of the complement $\overline{\Mfib}$ of the set $\Mfib$ of fibbinary numbers in the set of positive natural numbers Show Chinese title

Title: 在正自然数集合中，fibbinary数集合$\Mfib$的补集$\overline{\Mfib}$的结构

A.J.Macfarlane

Comments: 8 pages, 4 Tables

Subjects: Number Theory (math.NT)

[133] arXiv:2406.12561 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A positive density of elliptic curves are diophantine stable in certain Galois extensions Show Chinese title

Title: 某些伽罗瓦扩张中，椭圆曲线具有正密度的丢番图稳定性

Anwesh Ray, Pratiksha Shingavekar

Comments: Version 1: 23 pages

Subjects: Number Theory (math.NT)

[134] arXiv:2406.12758 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Small solutions to inhomogeneous and homogeneous quadratic congruences modulo prime powers Show Chinese title

Title: 模素数幂的非齐次与齐次二次同余的小解

Stephan Baier, Arkaprava Bhandari, Anup Haldar

Comments: 20 pages

Subjects: Number Theory (math.NT)

[135] arXiv:2406.13013 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: A lower bound for classical Kloosterman sums and an application Show Chinese title

Title: 经典Kloosterman和的下界及其应用

Stephan Baier, Jishu Das, Jewel Mahajan

Comments: 12 pages, revised

Subjects: Number Theory (math.NT)

[136] arXiv:2406.13255 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: P-adic Poissonian Pair Correlations via the Monna Map Show Chinese title

Title: 通过Monna映射的P进泊松对相关性

Christian Weiß

Subjects: Number Theory (math.NT)

[137] arXiv:2406.13278 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Mean Values of the auxiliary function Show Chinese title

Title: 辅助函数的均值

Juan Arias de Reyna

Comments: 9 pages, 1 figure

Subjects: Number Theory (math.NT)

[138] arXiv:2406.13334 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On Telhcirid's theorem on arithmetic progressions Show Chinese title

Title: 论特尔希里德关于等差数列的定理

Gautami Bhowmik, Yuta Suzuki

Comments: 28 pages

Subjects: Number Theory (math.NT)

[139] arXiv:2406.13630 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: AGZT-Lectures on formal multiple zeta values Show Chinese title

Title: AGZT-关于形式多重zeta值的讲座

Annika Burmester, Niclas Confurius, Ulf Kühn

Comments: Comments are welcome

Subjects: Number Theory (math.NT)

[140] arXiv:2406.13976 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Euler factors of equivariant $L$--functions of Drinfeld modules and beyond Show Chinese title

Title: Euler因子的等变$L$-函数和更广泛的德林舍尔模

Cristian D. Popescu, Nandagopal Ramachandran

Subjects: Number Theory (math.NT)

[141] arXiv:2406.14032 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Can the quadratrix truly square the circle? Show Chinese title

Title: 四边形真的能求出圆的面积吗？

Luis Cruz, Sergiy Koshkin

Comments: 18 pages, 7 figures

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

[142] arXiv:2406.14221 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On unsolvable equations of prime degree Show Chinese title

Title: 关于不可解的素数次数方程

Juliusz Brzeziński, Jan Stevens

Comments: 1 figure

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

[143] arXiv:2406.14254 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Shimura lift of Rankin-Cohen brackets of eigenforms and theta series Show Chinese title

Title: 特征形式和θ级数的Rankin-Cohen括号的Shimura提升

Wei Wang

Subjects: Number Theory (math.NT)

[144] arXiv:2406.14280 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Eichler-Selberg relations for singular moduli Show Chinese title

Title: Eichler-Selberg 关系式对于奇异模数

Yuqi Deng, Toshiki Matsusaka, Ken Ono

Comments: 21 pages

Subjects: Number Theory (math.NT)

[145] arXiv:2406.14339 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Mixed multiquadratic splitting fields Show Chinese title

Title: 混合多元二次分裂域

Fatma Kader Bingöl, Adam Chapman, Ahmed Laghribi

Comments: 7 pages

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

[146] arXiv:2406.14353 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Isolated and parameterized points on curves Show Chinese title

Title: 孤立和参数化的曲线上的点

Bianca Viray, Isabel Vogt

Comments: 37 pages. Minor edits to Section 4.3.1, Definition 4.3.10, Example 4.3.12, and Theorem 6.0.1

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

[147] arXiv:2406.14543 (cross-list from math.NT) [cn-pdf, pdf, other]

Title: Equivariant Vector Bundles with Connection on Drinfeld Symmetric Spaces Show Chinese title

Title: 等变向量丛与在德林费尔德对称空间上的连接

James Taylor

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

[148] arXiv:2406.14632 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Some new infinite families of non-$p$-rational real quadratic fields Show Chinese title

Title: 一些新的非$p$-有理实二次域的无限族

Gary McConnell

Comments: 11 pages

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

[149] arXiv:2406.14659 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: Algebraic proof of modular form inequalities for optimal sphere packings Show Chinese title

Title: 代数证明关于最优球体填充的模形式不等式

Seewoo Lee

Comments: 20+7 pages. Sage codes are removed from Appendix A and hand-checkable proofs are added as Appendix B. Comments are welcome!

Subjects: Number Theory (math.NT)

[150] arXiv:2406.14824 (cross-list from math.NT) [cn-pdf, pdf, html, other]

Title: On the minimal period of integer tilings Show Chinese title

Title: 关于整数铺砌的最小周期

Izabella Łaba, Dmitrii Zakharov

Comments: 7 pages. Added a remark in Section 2 and corrected some typos

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