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arXiv · 2301.05348

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

Mahdi Asgari·Kwangho Choiy
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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.

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Mahdi Asgari, Kwangho Choiy. 2023-01-13. Representations of the $p$-Adic $GSpin_4$ and $GSpin_6$ and the Adjoint L-Function. https://doi.org/10.1016/j.jnt.2024.06.004

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