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

Let π and π^' be cuspidal automorphic representations of GL(n) and GL(n^') with unitary central characters. We establish a new zero-free region for all GL(1)-twists of the Rankin-Selberg L-function L(s, π × π^'), generalizing Siegel's celebrated work on Dirichlet L-functions. As an application, we prove the first unconditional Siegel-Walfisz theorem for the Dirichlet coefficients of -L^'(s, π × π^')/L(s, π × π^'). Also, for n ≤ 8, we extend the region of holomorphy and nonvanishing for the twisted symmetric power L-functions L(s, π, Symⁿ ⊗χ) of any cuspidal automorphic representation of GL(2).