Algebraicity and the $p$-adic Interpolation of Special $L$-values for certain Classical Groups
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915230075846656 |
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| author | Jin, Yubo |
| author_facet | Jin, Yubo |
| contents | In this paper, we calculate the ramified local integrals in the doubling method and present an integral representation of standard $L$-functions for classical groups. We explicitly construct local sections of Eisenstein series such that the local ramified integrals represent certain ramified $L$-factors. As an application, we prove algebraicity of special $L$-values and construct $p$-adic $L$-functions for symplectic, unitary, quaternionic unitary and quaternionic orthogonal groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19113 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Algebraicity and the $p$-adic Interpolation of Special $L$-values for certain Classical Groups Jin, Yubo Number Theory 11F67, 11F55 In this paper, we calculate the ramified local integrals in the doubling method and present an integral representation of standard $L$-functions for classical groups. We explicitly construct local sections of Eisenstein series such that the local ramified integrals represent certain ramified $L$-factors. As an application, we prove algebraicity of special $L$-values and construct $p$-adic $L$-functions for symplectic, unitary, quaternionic unitary and quaternionic orthogonal groups. |
| title | Algebraicity and the $p$-adic Interpolation of Special $L$-values for certain Classical Groups |
| topic | Number Theory 11F67, 11F55 |
| url | https://arxiv.org/abs/2305.19113 |