标题:On automorphic analogues of the Möbius randomness principle
作者:Jiang Y.; Lü G.
作者机构:[Jiang, Y] School of Mathematics and Statistics, Shandong University, Weihai, Weihai, Shandong 264209, China;[ Lü, G] School of Mathematics, Shandong 更多
通讯作者:Lü, G(gslv@sdu.edu.cn)
通讯作者地址:[Lü, G] School of Mathematics, Shandong UniversityChina;
来源:Journal of Number Theory
出版年:2019
卷:197
页码:268-296
DOI:10.1016/j.jnt.2018.08.014
关键词:Fourier coefficients; Hecke–Maass forms; Möbius function; Strong orthogonality
摘要:Let F(z) be a Hecke–Maass form for SL(3,Z) (or SL(2,Z)), AF(n,1) (or AF(n)) be its Fourier coefficients, and L(s,F) the Godement–Jacquet L-function attached to F. And let μF(n) be the coefficients of the reciprocal of L(s,F) in the absolutely convergent region ℜs>1. In this paper we prove that μF(n) is strongly orthogonal to 1-step nilsequence. As applications, we prove that the Möbius function μ(n) is strongly orthogonal to AF(n,1)e(nα) and AF(n)2e(nα). More precisely, we establish ∑n≤Nμ(n)AF(n,1)e(nα)≪cNexp⁡(−clog⁡N), and ∑n≤Nμ(n)AF(n)2e(nα)≪AN(log⁡N)−A. Moreover, we also show that μF(n) is asymptotically orthogonal to any AC0(d) function, and all MMA and MMLS flows. © 2018 Elsevier Inc.
收录类别:SCOPUS
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85053723018&doi=10.1016%2fj.jnt.2018.08.014&partnerID=40&md5=d9349c668162d0e6597f8499c85d5628
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