Effective Multiplicity One for GL(n)

Details Effective Multiplicity One for GL(n) Effective Multiplicity One for GL(n)

2003-06-03

arxiv.org/abs/math/0306052v4

Mathematics

Number Theory

In this final version of this paper, soon to be published in this form in the American Journal of Math, I have corrected some

Scientific paper

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.

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