Standard zero-free regions for Rankin–Selberg L-functions via sieve theory

By Peter Humphries, Farrell Brumley. Mathematische Zeitschrift, 2017

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We give a simple proof of a standard zero-free region in the t-aspect for the Rankin–Selberg L-function $$L(s,\pi \times \widetilde{\pi })$$L(s,π×π~) for any unitary cuspidal automorphic representation $$\pi $$π of $$\mathrm {GL}_n(\mathbb {A}_F)$$GLn(AF) that is tempered at every nonarchimedean place outside a set of Dirichlet density zero.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8bc77a763d9af6bb8c8e3eac7df5224fe4163201