标题:Sums of absolute values of cusp form coefficients and their application
作者:Lu, Guangshi
作者机构:[Lu, GS]Shandong Univ, Dept Math, Jinan 250100, Shandong, Peoples R China.
通讯作者:Lu, GS
通讯作者地址:[Lu, GS]Shandong Univ, Dept Math, Jinan 250100, Shandong, Peoples R China.
来源:JOURNAL OF NUMBER THEORY
出版年:2014
卷:139
页码:29-43
DOI:10.1016/j.jnt.2013.12.011
关键词:Fourier coefficients of cusp forms; Symmetric power L-function;; Sato-Tate conjecture
摘要:Let S-k (Gamma) be the space of holomorphic cusp forms of even integral weight k for the full modular group. Let lambda f(n), lambda g(n) and lambda h (n) be the nth normalized Fourier coefficients of three holomorphic Hecke cusp forms f(z),g(z),h(z) is an element of S-k(Gamma), S-k1 (Gamma) and s(k2) (Gamma) respectively. In this paper we consider several averages of absolute values of Fourier coefficients of holomorphic Hecke cusp forms. In particular, we have (under suitable conditions); Sigma n <= x vertical bar lambda f(n)lambda g(n)vertical bar << x(log x)-20/3, Sigma n <= x vertical bar lambda f(n)lambda g(n)lambda h(n)vertical bar << x(log x)-0/3,; where and throughout this paper; theta= 1-8/3 pi = 0.1512....; As an application, we consider sums of coefficients of the Rankin-Selberg L-function and the triple product L-function, and prove that G. Lu / Journal of Number Theory 139 (2014) 29-43; Sigma n <= x lambda f(n)lambda g(n)<< x(3/5) (log x)(-20/30), Sigma n <=lambda f(n)lambda g(n)lambda h(n)<< x(7/9) (log x)-(0/3); and other similar results. (C) 2014 Elsevier Inc. All rights reserved.
收录类别:SCOPUS;SCIE
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-84894258278&doi=10.1016%2fj.jnt.2013.12.011&partnerID=40&md5=8da4a5a43df9931c5c205ffadd82278d
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