Lower Bounds for Rankin-Selberg $L$-functions on the Edge of the Critical Strip

Let $F$ be a number field, and let ${\pi }_1$ and ${\pi }_2$ be distinct unitary cuspidal automorphic representations of ${\mathrm{GL}}_{n_1}({\mathbb{A}}_F)$ and ${\mathrm{GL}}_{n_2}({\mathbb{A}}_F)$ respectively. In this paper, we derive new lower bounds for the Rankin-Selberg $L$-function $L(s,{\pi }_1\times {\tilde{\pi }}_2)$ along the edge $\mathrm{\Re }s=1$ of the critical strip in the $t$-aspect. The corresponding zero-free region for $L(s,{\pi }_1\times {\tilde{\pi }}_2)$ is also determined.