Conjectures about distinction and Asai $L$-functions of generic representations of general linear groups over local fields

Details Conjectures about distinction and Asai $L$-functions of generic representations of general linear groups over local fields Conjectures about distinction and Asai $L$-functions of generic representations of general linear groups over local fields

2008-11-10

arxiv.org/abs/0811.1410v3

Mathematics

Representation Theory

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Conjectures about distinction and Asai $L$-functions of generic representations of general linear groups over local fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Conjectures about distinction and Asai $L$-functions of generic representations of general linear groups over local fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conjectures about distinction and Asai $L$-functions of generic representations of general linear groups over local fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-724540