Langlands-Shahidi $L$-functions for $GSpin$ groups and the generic Arthur packet conjecture

TL;DR

This paper establishes that Langlands-Shahidi $L$-functions for $GSpin$ groups are Artin $L$-functions via the local Langlands correspondence, and applies this to improve understanding of the generic Arthur packet conjecture.

Contribution

It proves the Artin nature of certain $L$-functions for $GSpin$ groups and advances the weak generic Arthur packet conjecture using local $L$-packet descriptions.

Findings

$L$-functions for $GSpin$ groups are Artin $L$-functions.

A description of local $L$-packets containing generic members.

Strengthening of the weak generic Arthur packet conjecture.

Abstract

We prove that $L$-functions from Langlands-Shahidi method in the case of $GSpin$ groups over a non-Archimedean local field of characteristic zero are Artin $L$-functions through the local Langlands correspondence. It has an application on the proof of a weak version of the generic Arthur packet conjecture. Furthermore, we study and describe a local $L$-packet that contains a generic member in the case of $GSpin$ groups. Using this description of a local $L$-packet, we strengthen a weak version of the generic Arthur packet conjecture in those cases (local version of the generalized Ramanujan conjecture).