Distinguished representations and exceptional poles of the Asai-L-functionReport as inadecuate

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1 IMJ - Institut de Mathématiques de Jussieu

Abstract : In this article, we prove that it is equivalent for a generic irreducible representation of GLn,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 GL2,K, in particular we give a formula for Asai L-functions of principal series representations of GL2,K.

Author: Nadir Matringe -

Source: https://hal.archives-ouvertes.fr/


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