Distinguished representations and exceptional poles of the Asai-L-function

Details Distinguished representations and exceptional poles of the Asai-L-function Distinguished representations and exceptional poles of the Asai-L-function

2008-07-17

arxiv.org/abs/0807.2748v5

Mathematics

Representation Theory

Scientific paper

In this article, we proove that it is equivalent for a generic irreducible representation of GL(n,K), with K a p-adic field, to be distinguished, and for its Rankin-Selberg Asai L-function to have an exceptional pole at zero. This extends a criterion of Kable claiming that a discrete series representation is distinguished if and only if its Asai L-function has a pole at zero. As an application we compute by local methods Asai L-functions of ordinary representations of GL(2,K), in particular we give a formula for Asai L-functions of principal series representations of GL(2,K).

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