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

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

2009-10-19

arxiv.org/abs/0910.3660v1

Mathematics

Number Theory

submitted to the canadian mathematical bulletin 10-09

Scientific paper

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

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