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Effective multiplicity one on GLn and narrow zero-free regions for Rankin-Selberg L-functions
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 128, Number 6, December 2006
- pp. 1455-1474
- 10.1353/ajm.2006.0042
- Article
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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.