Arithmetic volume of Shtukas and Langlands duality
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915916132909056 |
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| author | Wang, Zeyu Wei, Wenqing |
| author_facet | Wang, Zeyu Wei, Wenqing |
| contents | We extend the work of Feng--Yun--Zhang relating the arithmetic volume of Shtukas with derivatives of zeta functions by allowing arbitrary coweights for split semisimple algebraic groups. As in their original work, the formula involves some numbers called eigenweights. We obtain uniform formulas for the eigenweights in terms of the Langlands dual group, marking the first structural role for the dual group in such formulas governing derivatives of L-functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03763 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Arithmetic volume of Shtukas and Langlands duality Wang, Zeyu Wei, Wenqing Number Theory Algebraic Geometry Representation Theory We extend the work of Feng--Yun--Zhang relating the arithmetic volume of Shtukas with derivatives of zeta functions by allowing arbitrary coweights for split semisimple algebraic groups. As in their original work, the formula involves some numbers called eigenweights. We obtain uniform formulas for the eigenweights in terms of the Langlands dual group, marking the first structural role for the dual group in such formulas governing derivatives of L-functions. |
| title | Arithmetic volume of Shtukas and Langlands duality |
| topic | Number Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2604.03763 |