Resonances and Ω-results for exponential sums related to Maass forms for SL(n, Z)

被引：9

作者：

Ernvall-Hytonen, Anne-Maria ^{[1
]}

Jaasaari, Jesse ^{[1
]}

Vesalainen, Esa V. ^{[1
]}

机构：

[1] Univ Helsinki, Dept Math & Stat, FIN-00014 Helsinki, Finland

来源：

JOURNAL OF NUMBER THEORY | 2015年 / 153卷

基金：

芬兰科学院;

关键词：

Exponential sums; Fourier coefficients of automorphic forms; GL(n) Maass forms; Codement-Jacquet L-functions; Voronoi-type summation formulae; FOURIER COEFFICIENTS; MULTIPLICITY ONE; ADDITIVE TWISTS; ZEROS;

D O I：

10.1016/j.jnt.2015.01.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain resonances for short exponential sums weighted by Fourier coefficients of Maass forms for SL(n, Z). This involves deriving asymptotics for the integrals appearing in the GL(n) Voronoi summation formula. As an application, we also prove an Omega-result for short sums of Fourier coefficients. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：135 / 157

页数：23

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