Lower bounds for Rankin–Selberg $L$-functions on the edge of the critical strip
Volume 211 / 2023
Acta Arithmetica 211 (2023), 161-171
MSC: Primary 11M26; Secondary 11F66.
DOI: 10.4064/aa221111-14-7
Published online: 12 October 2023
Abstract
Let $F$ be a number field, and let $\pi _1$ and $\pi _2$ be distinct unitary cuspidal automorphic representations of ${\rm GL}_{n_1}(\mathbb {A}_F)$ and ${\rm GL}_{n_2}(\mathbb {A}_F)$ respectively. We derive new lower bounds for the Rankin–Selberg $L$-function $L(s, \pi _1 \times \widetilde {\pi }_2)$ along the edge $\Re s = 1$ of the critical strip in the $t$-aspect. The corresponding zero-free region for $L(s, \pi _1 \times \widetilde {\pi }_2)$ is also determined.
