Abstract

We establish zero-free regions tapering as an inverse power of the analytic conductor for Rankin-Selberg L-functions on GLn×GLn'. Such zero-free regions are equivalent to commensurate lower bounds on the edge of the critical strip, and in the case of L(s, π X), on the residue at s = 1. As an application we show that a cuspidal automorphic representation on GLn 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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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1455-1474
Launched on MUSE
2006-12-11
Open Access
N

Copyright

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