Uniform Integrality of critical values of the Rankin-Selberg $L$-function for ${\rm GL}_{n}\times {\rm GL}_{n-1}$
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913296245850112 |
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| author | Hara, Takashi Miyazaki, Tadashi Namikawa, Kenichi |
| author_facet | Hara, Takashi Miyazaki, Tadashi Namikawa, Kenichi |
| contents | After introducing the notion of uniform integrality of critical values of the Rankin-Selberg $L$-functions for $\mathrm{GL}_{n}\times \mathrm{GL}_{n-1}$, we study it when the base field is totally imaginary. For this purpose, we adopt specific models of highest weight representations of the general linear groups, construct the Eichler-Shimura classes for $\mathrm{GL}_{n}$ and $\mathrm{GL}_{n-1}$ in an explicit manner, and then evaluate the cohomological cup product of them, by making the best use of Gel'fand-Tsetlin basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12200 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uniform Integrality of critical values of the Rankin-Selberg $L$-function for ${\rm GL}_{n}\times {\rm GL}_{n-1}$ Hara, Takashi Miyazaki, Tadashi Namikawa, Kenichi Number Theory After introducing the notion of uniform integrality of critical values of the Rankin-Selberg $L$-functions for $\mathrm{GL}_{n}\times \mathrm{GL}_{n-1}$, we study it when the base field is totally imaginary. For this purpose, we adopt specific models of highest weight representations of the general linear groups, construct the Eichler-Shimura classes for $\mathrm{GL}_{n}$ and $\mathrm{GL}_{n-1}$ in an explicit manner, and then evaluate the cohomological cup product of them, by making the best use of Gel'fand-Tsetlin basis. |
| title | Uniform Integrality of critical values of the Rankin-Selberg $L$-function for ${\rm GL}_{n}\times {\rm GL}_{n-1}$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2308.12200 |