p-adic interpolation of Gauss--Manin connections on nearly overconvergent modular forms and p-adic L-functions

Fuente: arXiv
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Main Authors: Graham, Andrew, Pilloni, Vincent, Jacinto, Joaquín Rodrigues
Format: Preprint
Published: 2023
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_version_ 1866915604808597504
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
id 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