A Standard Zero Free Region for Rankin Selberg L-functions
نویسندگان
چکیده
A standard zero free region is obtained for Rankin Selberg L-functions L(s, f×f) where f is a tempered Maass form on GL(n) and f is not necessarily self dual. The method is based on the theory of Eisenstein series generalizing a work of Sarnak. §
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We give a narrow zero-free region for standard L-functions on GL(n) and Rankin-Selberg L-functions on GL(m) × GL(n) through the use of positive Dirichlet series. Such zero-free regions are equivalent to lower bounds on the edge of the critical strip, and in the case of L(s, π × ˜ π), on the residue at s = 1. Using the latter we show that a cuspidal automorphic representation on GL(n) is determi...
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