Effective Multiplicity One for GL(n)
Abstract
Description
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.
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
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