Average behavior of Fourier coefficients of Maass cusp forms for hyperbolic -manifolds

被引：0

作者：

Jiang, Yujiao ^{[1
]}

Lu, Guangshi ^{[1
]}

机构：

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

来源：

MONATSHEFTE FUR MATHEMATIK | 2015年 / 178卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Fourier coefficients; Maass cusp forms; Hyperbolic; 3-manifolds; RAMANUJAN CONJECTURE; PLANCHEREL MEASURES; EULER PRODUCTS; SERIES; CLASSIFICATION;

D O I：

10.1007/s00605-015-0766-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let lambda(phi)(n) be the n-th Fourier coefficient of a doubly even and normalized Hecke-Maass cusp form for hyperbolic 3-manifolds. In this paper, we investigate the behavior of summatory functions in the following (i) the j-th power sum of lambda(phi)(n) Sigma(N(n)<= x)lambda(phi)(n)(j), where j <= 8; (ii) the sum of lambda(phi)(n) over the sparse sequence n(l) Sigma(N(n)<= x)lambda(phi)(n)(l), where l <= 4; (iii) the hybrid sum for lambda(phi)(n) Sigma(N(n)<= x)lambda(phi)(n(l))(j), where 2 <= l <= 4, j = 2, or l = 2, j = 4.

引用

页码：221 / 236

页数：16