Power moments of Hecke eigenvalues for congruence group

JOURNAL OF NUMBER THEORY

卷:198

Article

Song, Ping¹  Zhai, Wenguang²  Zhang, Deyu¹ 

[1] Shandong Normal Univ, Sch Math & Stat, Jinan 250014, Shandong, Peoples R China

[2] China Univ Min & Technol, Dept Math, Beijing 100083, Peoples R China

关键词: Hecke eigenvalues;    Holomorphic cusp forms;    Arithmetic progressions;   

DOI  :  10.1016/j.jnt.2018.10.006

来源: Elsevier

【 摘 要 】

Let H-l(N) be the set of normalized primitive holomorphic cusp forms of even integral weight l for the congruence group Gamma(0)(N). For any f is an element of H-l(N), we study the higher power moments of S-f(x; N) := Sigma(n <= x) lambda(f)(n) and derive the asymptotic formulas for integral S-T(1)f(k)(x; N)dx, k = 2,3, ... 7, by using Ivic's large value arguments, where lambda(f)(n) is the n-th Hecke eigenvalue of f. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free