For positive integers m,m’, let π and π’ be cuspidal automorphic representations of GL(m) and GL(m’), respectively. In this talk, I will present a new simple proof of zero-free regions for the L-function L(s, π) and for the Rankin–Selberg L-function L(s, π x π’) given that π, π’ or L(s, π \times π’) is self-dual. Our approach builds on ideas of “pretentious” multiplicative functions due to Granville and Soundararajan (as presented by Koukoulopoulos).
Talk by Nawapan Wattanawanichkul