Distinguished representations and exceptional poles of the Asai-L-function
Representation Theory
2008-11-04 v5
Abstract
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).
Cite
@article{arxiv.0807.2748,
title = {Distinguished representations and exceptional poles of the Asai-L-function},
author = {Nadir Matringe},
journal= {arXiv preprint arXiv:0807.2748},
year = {2008}
}