A generalization of Tatuzawa's theorem to Rankin-Selberg L-functions

In 2023, Jesse Thorner and I established a new zero-free region for all $GL(1)$-twists of $GL(m) \times GL(n)$ Rankin-Selberg $L$-functions, generalizing Siegel's celebrated work on Dirichlet $L$-functions. In the talk, I will discuss our recent strengthening of this result, which generalizes Tatuzawa's refinement of Siegel's theorem.