High power sums of Fourier coefficients of holomorphic cusp forms and their applications

被引：0

作者：

Hu, Guangwei ^{[1
]}

Lao, Huixue ^{[1
]}

Pan, Huimin ^{[1
]}

机构：

[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250358, Peoples R China

来源：

AIMS MATHEMATICS | 2024年 / 9卷 / 09期

基金：

中国国家自然科学基金;

关键词：

cusp form; L-function; Fourier coefficient; sign change; SIGN CHANGES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let lambda(f)(n) be the nth normalized Fourier coefficient of a holomorphic cusp form f for the full modular group. In this paper, we established asymptotic formulae for high power sums of Fourier coefficients of cusp forms and further improved previous results. Moreover, as an application, we studied the signs of the sequences {lambda(f)(n)} and {lambda(f)(n)lambda(g)(n)} in short intervals, and presented some quantitative results for the number of sign changes for n <= x.

引用

页码：25166 / 25183

页数：18

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