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Mean value theorem connected with Fourier coefficients of Hecke-Maass forms for SL(m, ℤ)

Published online by Cambridge University Press:  25 April 2016

YUJIAO JIANG ,
GUANGSHI LÜ  and
XIAOFEI YAN
YUJIAO JIANG
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, China. e-mails: yujiaoj@hotmail.com
GUANGSHI LÜ
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, China. e-mails: gslv@sdu.edu.cn
XIAOFEI YAN
Affiliation:
School of Mathematics, Shandong Normal University, Jinan, Shandong 250014, China. e-mails: xfyan.sdu@gmail.com
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Abstract

Let F(z) be a Hecke–Maass form for SL(m, ℤ) with m ⩽ 3, or be the symmetric power lift of a Hecke–Maass form for SL(2, ℤ) if m = 4, 5 and let AF(n, 1, . . ., 1) be the coefficients of L-function attached to F. We establish

$$\sum_{q\leq Q}\max_{(a,q)=1}\max_{y\leq x}\left|\sum_{n\leq y \atop n\equiv a\bmod q}A_F(n,1, \dots, 1)\Lambda(n)\right| \ll x\log^{-A}x,$$
where Q = xϑ−ϵ with some ϑ > 0, the implied constant depends on F, A, ϵ.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 2 , September 2016 , pp. 339 - 356
Copyright
Copyright © Cambridge Philosophical Society 2016 

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