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Transactions of the American Mathematical Society

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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
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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