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arXiv · 1703.05450

Standard Zero-Free Regions for Rankin--Selberg L-Functions via Sieve Theory

Peter Humphries
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Abstract

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

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Peter Humphries. 2017-12-10. Standard Zero-Free Regions for Rankin--Selberg L-Functions via Sieve Theory. https://doi.org/10.1007/s00209-018-2136-8

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