Effective Multiplicity One for GL(n)
Abstract
We establish zero-free regions tapering as an inverse power of the analytic conductor for Rankin-Selberg L-functions on GL(n) x GL(n'). Such zero-free regions are equivalent to commensurate lower bounds on the edge of the critical strip, and in the case of $L(s,f x f~), on the residue at s=1. As an application we show that a cuspidal automorphic representation on GL(n) is determined by a finite number of its Dirichlet series coefficients, and that this number grows at most polynomially in the analytic conductor.
Cite
@article{arxiv.math/0306052,
title = {Effective Multiplicity One for GL(n)},
author = {Farrell Brumley},
journal= {arXiv preprint arXiv:math/0306052},
year = {2007}
}
Comments
In this final version of this paper, soon to be published in this form in the American Journal of Math, I have corrected some definitions concerning the analytic conductor and addressed some minor problems involving ramification in the final section