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arXiv · 0911.0025

Solvable Base Change and Rankin-Selberg Convolutions

Tim Gillespie
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Abstract

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

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Tim Gillespie. 2009-10-30. Solvable Base Change and Rankin-Selberg Convolutions. https://arxiv.org/abs/0911.0025

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