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

Nadir Matringe (1)

1 IMJ - Institut de Mathématiques de Jussieu

In this article, we prove 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).

Domaines: Théorie des représentations [math.RT]

Nadir Matringe. Distinguished representations and exceptional poles of the Asai-L-function. 2008. ⟨hal-00299528v6⟩