Congruence classes for modular forms over small sets

IF 0.5 3区数学 Q3 MATHEMATICS International Journal of Number Theory Pub Date : 2024-04-06 DOI:10.1142/s1793042124500799

Subham Bhakta, Srilakshmi Krishnamoorthy, R. Muneeswaran

引用次数: 0

Abstract

Serre showed that for any integer $m, a (n) \equiv 0 (mod m)$ for almost all $n,$ where $a (n)$ is the $n th$ Fourier coefficient of any modular form with rational coefficients. In this paper, we consider a certain class of cuspforms and study $# {a (n) (mod m)}_{n \leq x}$ over the set of integers with $O (1)$ many prime factors. Moreover, we show that any residue class $a \in ℤ / m ℤ$ can be written as the sum of at most 13 Fourier coefficients, which are polynomially bounded as a function of $m .$

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小集合上模态的协整类

塞雷证明，对于任意整数 m，几乎所有 n 的 a(n)≡0(modm)，其中 a(n) 是任意有理系数模形式的第 n 个傅里叶系数。在本文中，我们考虑了某类余弦形式，并研究了在具有 O(1) 多质因数的整数集合上 #{a(n)(modm)}n≤x 的问题。此外，我们还证明了任何残差类 a∈ℤ/mℤ 都可以写成最多 13 个傅里叶系数之和，而这些系数作为 m 的函数是多项式有界的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.

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