paper

A Prime Number Theorem for Rankin-Selberg L-functions over Number fields

arXiv:0910.3660

Abstract

We prove a prime number theorem first for the classical Rankin-Selberg L-function $L (s, I ¨ \times I ¨ ^{'})$ over any Galois extension with $I ¨ $ and $I ¨ ^{'}$ unitary automorphic cuspidal representations of $G L_{n}$ and $G L_{m}$ respectively with at least one of the representations subject to a self-contragredient assumption. We then extend these results to two representations $I ¨ $ defined on $G L_{n} / E$ and $I ¨ ^{'}$ defined on $G L_{m} / F$ with $E$ and $F$ cylic algebraic number fields of coprime degree where $I ¨ $ and $I ¨ ^{'}$ admit a base change lift from $Q$ again given a self-contragredient assumption on at least one of the representations which lift to $I ¨ $ or $I ¨ ^{'}$ .

submitted to the canadian mathematical bulletin 10-09