The sixth and eighth moments of Fourier coefficients of cusp forms

被引：31

作者：

Lue, Guangshi ^{[1
]}

机构：

[1] Shandong Univ, Dept Math, Jinan 250100, Shandong, Peoples R China

来源：

JOURNAL OF NUMBER THEORY | 2009年 / 129卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Fourier coefficients of cusp forms; Symmetric power L-function; POWER L-FUNCTIONS; GL(2); 4TH;

D O I：

10.1016/j.jnt.2009.01.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let lambda(n) be the nth normalized Fourier coefficient of a holomorphic Hecke eigencuspform f(z) of even integral weight k for the full modular group. In this paper we are able to prove the following results. (i) For any epsilon > 0, we have Sigma(n <= x) lambda(6)(n) = xP(1)(log x) + O(f,epsilon)(x(31/32+epsilon)), where P(1)(x) is a polynomial of degree 4. (ii) For any epsilon > 0, we have Sigma(n <= x)lambda(8)(n) = xP(2)(log x) + O(f,epsilon)(x(127/128+epsilon)), where P(2)(x) is a polynomial of degree 13 (C) 2009 Elsevier Inc All rights reserved

引用

页码：2790 / 2800

页数：11

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