Spectral large sieve inequalities for Hecke congruence subgroups of SL(2, Z[i])

被引：2

作者：

Watt, Nigel

机构：

来源：

JOURNAL OF NUMBER THEORY | 2014年 / 140卷

基金：

英国工程与自然科学研究理事会;

关键词：

Spectral theory; Large sieve; Hecke congruence group; Gaussian integers; Summation formula; Automorphic form; Cusp form; Non-holomorphic modular form; Fourier coefficient; Kloosterman sum; KLOOSTERMAN SUMS; FOURIER COEFFICIENTS; FORMS;

D O I：

10.1016/j.jnt.2014.01.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove, in respect of an arbitrary Hecke congruence subgroup Gamma = Gamma(0)(q(0)) <= SL(2,Z[i]), some new upper bounds for sums involving Fourier coefficients of Gamma-automorphic cusp forms on SL(2,C). The Fourier coefficients in question may arise from the Fourier expansion at any given cusp c of Gamma (our results are not limited to the case c = infinity). Our proof utilises an extension, to arbitrary cusps, of a spectral-Kloosterman summation formula for Gamma\SL(2,C) that was obtained by Lokvenec-Guleska (in her doctoral thesis). (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：349 / 424

页数：76

共 10 条

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