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.
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页码：488 / 494
页数：7
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