p-adic interpolation of Gauss--Manin connections on nearly overconvergent modular forms and p-adic L-functions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915604808597504 |
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| author | Graham, Andrew Pilloni, Vincent Jacinto, Joaquín Rodrigues |
| author_facet | Graham, Andrew Pilloni, Vincent Jacinto, Joaquín Rodrigues |
| contents | In this paper, we give a new geometric definition of nearly overconvergent modular forms and $p$-adically interpolate the Gauss-Manin connection on this space. This can be seen as an ``overconvergent'' version of the unipotent circle action on the space of $p$-adic modular forms, as constructed by Gouvêa and Howe. This improves on results of Andreatta--Iovita and has applications to the construction of Rankin--Selberg and triple product $p$-adic $L$-functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_14438 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | p-adic interpolation of Gauss--Manin connections on nearly overconvergent modular forms and p-adic L-functions Graham, Andrew Pilloni, Vincent Jacinto, Joaquín Rodrigues Number Theory 11F33, 11F67, 11F77 In this paper, we give a new geometric definition of nearly overconvergent modular forms and $p$-adically interpolate the Gauss-Manin connection on this space. This can be seen as an ``overconvergent'' version of the unipotent circle action on the space of $p$-adic modular forms, as constructed by Gouvêa and Howe. This improves on results of Andreatta--Iovita and has applications to the construction of Rankin--Selberg and triple product $p$-adic $L$-functions. |
| title | p-adic interpolation of Gauss--Manin connections on nearly overconvergent modular forms and p-adic L-functions |
| topic | Number Theory 11F33, 11F67, 11F77 |
| url | https://arxiv.org/abs/2311.14438 |