The average value of Fourier coefficients of cusp forms in arithmetic progressions

被引：9

作者：

Lue, Guangshi ^{[1
]}

机构：

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

来源：

JOURNAL OF NUMBER THEORY | 2009年 / 129卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Arithmetic progression; Cusp form; Fourier coefficient; RAMANUJAN FUNCTION; DIVISOR PROBLEM; SUMS;

D O I：

10.1016/j.jnt.2008.05.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Recently Blomer showed that if alpha(n) denote the normalized Fourier coefficients of any holomorphic cusp form f with integral weight, then [GRAPHICS] holds uniformly in q <= X. By an elementary argument we show that independent of q, [GRAPHICS] where alpha(n) could be the normalized Fourier coefficients of any reasonable cusp forms, including Maass cusp forms, holomorphic Cusp forms with half-integral or integral weights. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：488 / 494

页数：7

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