Solvable Base Change and Rankin-Selberg Convolutions

Details Solvable Base Change and Rankin-Selberg Convolutions Solvable Base Change and Rankin-Selberg Convolutions

2009-10-30

arxiv.org/abs/0911.0025v1

Mathematics

Number Theory

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

Scientific paper

Given unitary automorphic cuspidal representations $\pi$ and $\pi'$ 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 $L(s,AI_{E/\mathbb{Q}}(\pi)\times AI_{F/\mathbb{Q}}(\pi'))$ 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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