Representations of the $p$-Adic $GSpin_4$ and $GSpin_6$ and the Adjoint L-Function

Mahdi Asgari; Kwangho Choiy

doi:10.1016/j.jnt.2024.06.004

paper

Representations of the $p$ -Adic $GS p i n_{4}$ and $GS p i n_{6}$ and the Adjoint L-Function

arXiv:2301.05348 · doi:10.1016/j.jnt.2024.06.004

Abstract

We prove a conjecture of B. Gross and D. Prasad about determination of generic $L$ -packets in terms of the analytic properties of the adjoint $L$ -function for $p$ -adic general even spin groups of semi-simple ranks 2 and 3. We also explicitly write the adjoint $L$ -function for each $L$ -packet in terms of the local Langlands $L$ -functions for the general linear groups.

Abstract, introduction and the bibliography slightly updated; removed some typos

References in corpus (1)

Branching laws for Classical Groups: the non-tempered case

Representations of the p-Adic GSpin4​ and GSpin6​ and the Adjoint L-Function

Abstract

References in corpus (1)

Representations of the $p$ -Adic $GS p i n_{4}$ and $GS p i n_{6}$ and the Adjoint L-Function