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arXiv · 0910.3660

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

Tim Gillespie·Guanghua Ji
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Abstract

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

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Tim Gillespie, Guanghua Ji. 2009-10-19. A Prime Number Theorem for Rankin-Selberg L-functions over Number fields. https://arxiv.org/abs/0910.3660

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