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Langlands-Shahidi $L$-functions for $GSpin$ groups and the generic Arthur packet conjecture
Transactions of the American Mathematical Society ( IF 1.2 ) Pub Date : 2021-02-02 , DOI: 10.1090/tran/8258
Yeansu Kim

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).

中文翻译:

用于 $GSpin$ 组的 Langlands-Shahidi $L$ 函数和通用 Arthur 包猜想

我们通过局部朗兰兹对应证明在特征为零的非阿基米德局部域上的 $GSpin$ 群的情况下,Langlands-Shahidi 方法的 $L$-函数是 Artin$L$-函数。它在证明通用亚瑟包猜想的弱版本上有应用。此外,我们研究并描述了一个本地 $L$-packet,它包含 $GSpin$ 组的通用成员。使用本地 $L$-packet 的这种描述,我们在这些情况下加强了通用 Arthur 数据包猜想的弱版本(广义 Ramanujan 猜想的本地版本)。
更新日期:2021-02-02
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