Effective multiplicity one on GLN and narrow zero-free regions for Rankin-Selberg L-functions

被引:61
作者
Brumley, Farrell [1 ]
机构
[1] Univ Montpellier 2, UMR 5149, CNRS, I3M, F-34095 Montpellier 05, France
关键词
D O I
10.1353/ajm.2006.0042
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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, pi x pi), 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.
引用
收藏
页码:1455 / 1474
页数:20
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