On the Asymptotic Distribution of Fourier Coefficients of Cusp Forms

被引：12
|
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).
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页数：17
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