On the Asymptotic Distribution of Fourier Coefficients of Cusp Forms

被引：16

作者：

Liu, Huafeng ^{[1
]}

机构：

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

来源：

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY | 2023年 / 54卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Fourier coefficients; Cusp forms; Variance; AVERAGE BEHAVIOR; POWER SUMS; SQUARE;

D O I：

10.1007/s00574-023-00335-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let. lambda(f) (n) be the n-th normalized Fourier coefficient of primitive holomorphic cusp form of even integral weight k >= 2 for the full modular group SL(2, Z). In this paper, we first refine related previous results on the l-th power sums of the Fourier coefficient lambda(f)(n). Then we establish asymptotic formulas of the variance of lambda(l)(f) (n).

引用

页数：17

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