Solvable Base Change and Rankin-Selberg Convolutions

Abstract

Given unitary automorphic cuspidal representations $\ddot{I}€$ and $\ddot{I}{€}^{\prime }$ defined on $G{L}_n({\mathbb{A}}_E)$ and $G{L}_m({\mathbb{A}}_F)$, respectively, with $E$ and $F$ solvable algebraic number fields we deduce a prime number theorem for the Rankin-Selberg L-function $L(s,A{I}_{E/\mathbb{Q}}(\ddot{I}€)\times A{I}_{F/\mathbb{Q}}(\ddot{I}{€}^{\prime }))$ under a self-contragredient assumption and a suitable Galois invariance condition on the representations, where $A{I}_{K/\mathbb{Q}}$ denotes the automorphic induction functor for any number field $K/\mathbb{Q}$.

Submitted to the Journal of Number Theory (10/30)