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

Kim, Yeansu

doi:10.1090/tran/8258

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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