Fourth power moment of coefficients of automorphic L-functions for GL(m)

作者：Jiang, Yujiao; Lu, Guangshi

来源：Forum Mathematicum, 2017, 29(5): 1199-1212.

DOI：10.1515/forum-2016-0097

• Coefficients of L-functions
• Maass cusp forms
• automorphic representation

Let pi be a unitary cuspidal automorphic representation for GL(m)(A(Q)), and let L(s, pi) be the automorphic L-function attached to pi, which has a Dirichlet series expression in the half-plane Rs > 1, i.e. @@@ L(s,pi) = Sigma(infinity)(n=1) lambda pi(n)/n(s). @@@ In this paper we are interested in the upper bound of the fourth power moment of lambda pi(n), i.e. Sigma(n <= x) lambda(pi)(n)(4). If m = 2, we are able to consider the sixteenth power moment of lambda(pi)(n). As an application, we consider the lower bound of Sigma(n <= x)vertical bar lambda(pi)(n)vertical bar, which improves previous results.

• 出版日期2017-9
• 单位山东大学