The generalized prime number theorem for automorphic L-functions

Abstract

Let π and π′ be automorphic irreducible cuspidal representations of GLm(ℚ\( \mathbb{Q}_\mathbb{A} \)) and GLm′ (ℚ\( \mathbb{Q}_\mathbb{A} \)), respectively, and L(s, π × \( \tilde \pi ' \)) be the Rankin-Selberg L-function attached to π and π′. Without assuming the Generalized Ramanujan Conjecture (GRC), the author gives the generalized prime number theorem for L(s, π × \( \tilde \pi ' \)) when π ≅ π′. The result generalizes the corresponding result of Liu and Ye in 2007.