A new zero-free region for Rankin-Selberg $L$-functions

I will present a new zero-free region for all $\mathrm{GL}(1)$-twists of $\mathrm{GL}(m)\times\mathrm{GL}(n)$ Rankin-Selberg $L$-functions. The proof is inspired by Siegel's celebrated lower bound for Dirichlet $L$-functions at $s = 1$.

This is joint work with Jesse Thorner.