THE AVERAGE BEHAVIOR OF FOURIER COEFFICIENTS OF CUSP FORMS OVER SPARSE SEQUENCES

被引：27
|
作者：
Lao, Huixue [1 ]
Sankaranarayanan, Ayyadurai [2 ,3 ]
机构：
[1] Shandong Normal Univ, Dept Math, Jinan 250014, Shandong, Peoples R China
[2] Univ Ulm, Inst Number Theory & Probabil Theory, D-89069 Ulm, Germany
[3] Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2009年 / 137卷 / 08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; Rankin-Selberg L-function; POWER L-FUNCTIONS; GL(2); SQUARE;
D O I：
10.1090/S0002-9939-09-09855-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let lambda(n) be the nth normalized Fourier coefficient of a holomorphic Hecke eigenform f(z) is an element of S-k(Gamma) In this paper we are interested in the average behavior of lambda(2)(n) over sparse sequences. By using the properties of symmetric power L-functions and their Rankin-Selberg L-functions, we are able to establish that for any epsilon > 0, Sigma(n <= x) lambda(2)(n(j)) = c(j-1)x + O (x(1-2/(j+1)2+2) (+ epsilon)) , where j = 2, 3,4.
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页码：2557 / 2565
页数：9
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