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

We prove, in respect of an arbitrary Hecke congruence subgroup \Gamma =\Gamma_0(q_0) of the group SL(2,Z[i]), some new upper bounds (or `spectral large sieve inequalities') for sums involving Fourier coefficients of \Gamma -automorphic cusp forms on SL(2,C). The Fourier coefficients in question...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2013-02
Main Author: Watt, Nigel
Format: Article
Language:English
Subjects:
Cusps
Inequalities
Spectra
Subgroups
Upper bounds
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove, in respect of an arbitrary Hecke congruence subgroup \Gamma =\Gamma_0(q_0) of the group SL(2,Z[i]), some new upper bounds (or `spectral large sieve inequalities') 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 in which c is the cusp at infinity. For this reason, our proof is reliant upon an extension, to arbitrary cusps, of the spectral-Kloosterman sum formula for \Gamma\SL(2,C) obtained by Hristina Lokvenec-Guleska in her doctoral thesis (generalising the sum formulae of Roelof Bruggeman and Yoichi Motohashi for PSL(2,Z[i])\PSL(2,C) in several respects, though not as regards the choice of cusps). A proof of the required extension of the sum formula is given in an appendix.
ISSN:2331-8422
DOI:10.48550/arxiv.1302.3112