Langlands-Shahidi $L$-functions for $GSpin$ groups and the generic Arthur packet conjecture
Author:
Yeansu Kim
Journal:
Trans. Amer. Math. Soc. 374 (2021), 2559-2580
MSC (2000):
Primary 11F70; Secondary 22E50
DOI:
https://doi.org/10.1090/tran/8258
Published electronically:
February 2, 2021
MathSciNet review:
4223026
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We prove that Langlands-Shahidi $L$-functions in the case of $GSpin$ groups over a non-Archimedean local field of characteristic zero are Artin $L$-functions through the local Langlands correspondence. This has an application in 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 the case of $GSpin$ groups (i.e. a local version of the generalized Ramanujan conjecture).
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Additional Information
Yeansu Kim
Affiliation:
Department of Mathematics Education, Chonnam National University, Gwangju city, Korea
MR Author ID:
1094118
ORCID:
0000-0001-9427-6136
Email:
ykim@jnu.ac.kr
Keywords:
Langlands-Shahidi method,
the generic Arthur packet conjecture,
$L$-packet
Received by editor(s):
December 26, 2017
Received by editor(s) in revised form:
September 15, 2019, and May 27, 2020
Published electronically:
February 2, 2021
Additional Notes:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2017R1C1B2010081).
Article copyright:
© Copyright 2021
American Mathematical Society