Conjectures about distinction and Asai $L$-functions of generic representations of general linear groups over local fields
| dc.creator | Matringe, Nadir | |
| dc.date | 2008-11-10 | |
| dc.date | 2009-01-02 | |
| dc.date.accessioned | 2026-07-07T12:23:28Z | |
| dc.date.available | 2026-07-07T12:23:28Z | |
| dc.description | Let $K/F$ be a quadratic extension of p-adic fields. The Bernstein-Zelevinsky's classification asserts that generic representations are parabolically induced from quasi-square-integrable representations. We show, following a method developed by Cogdell and Piatetski-Shapiro, that the equality of the Rankin-Selberg type Asai $L$-function of generic representations of $GL(n,K)$ and of the Asai $L$-function of the Langlands parameter, is equivalent to the truth of a conjecture about classification of distinguished generic representations in terms of the inducing quasi-square-integrable representations. As the conjecture is true for principal series representations, this gives the expression of the Asai L-function of such representations. | |
| dc.identifier | https://arxiv.org/abs/0811.1410 | |
| dc.identifier | http://arxiv.org/abs/0811.1410 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213999 | |
| dc.subject | Representation Theory | |
| dc.subject | 22E50, 11S40 | |
| dc.title | Conjectures about distinction and Asai $L$-functions of generic representations of general linear groups over local fields | |
| dc.type | text |