$L$-packets and the generic Arthur packet conjectures for even unitary similitude groups
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908389360009216 |
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| author | Kim, Yeansu Krishnamurthy, Muthu Shahidi, Freydoon |
| author_facet | Kim, Yeansu Krishnamurthy, Muthu Shahidi, Freydoon |
| contents | We establish the generic local Langlands correspondence by showing the equality of the Langlands-Shahidi $L$-functions and Artin $L$-functions in the case of even unitary similitude groups. As an application, we prove both weak and strong versions of the generic Arthur packet conjectures in the cases of even unitary similitude groups and even unitary groups. We further describe (not necessarily generic) $L$-packets for even unitary similitude groups and establish their expected properties, including Shahidi's conjecture, the finiteness of $L$-packets, and other related results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00892 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L$-packets and the generic Arthur packet conjectures for even unitary similitude groups Kim, Yeansu Krishnamurthy, Muthu Shahidi, Freydoon Number Theory Primary 11F67, 11F66, 11F70, 11F75, 22E55 We establish the generic local Langlands correspondence by showing the equality of the Langlands-Shahidi $L$-functions and Artin $L$-functions in the case of even unitary similitude groups. As an application, we prove both weak and strong versions of the generic Arthur packet conjectures in the cases of even unitary similitude groups and even unitary groups. We further describe (not necessarily generic) $L$-packets for even unitary similitude groups and establish their expected properties, including Shahidi's conjecture, the finiteness of $L$-packets, and other related results. |
| title | $L$-packets and the generic Arthur packet conjectures for even unitary similitude groups |
| topic | Number Theory Primary 11F67, 11F66, 11F70, 11F75, 22E55 |
| url | https://arxiv.org/abs/2506.00892 |