Shifan Zhao
The Ohio State University
Title
Landau-Siegel Zeros of Rankin-Selberg L-functions
Abstract
Landau-Siegel zeros of L-functions are real zeros that are very close to 1. For Dirichlet L-functions, the existence (or non-existence) of such zeros is closely related to other arithmetic problems such as the class number problem, distribution of primes in arithmetic progressions, and non-vanishing of central values of twisted L-functions of holomorphic cusp forms. The Landau-Siegel zeros of automorphic L-functions $L(s,\pi)$ attached to automorphic representations $\pi$ on $GL(n)$ have been extensively studied in the last thirty years, starting with the ground-breaking work of Goldfeld, Hoffstein and Lieman. We study several families of Rankin-Selberg L-functions that are not yet known to be automorphic, and we prove unconditionally that they admit no Landau-Siegel zeros. As a corollary, we derive standard zero-free regions for these Rankin-Selberg L-functions without any exceptional zero. This is joint work with Jesse Thorner.
