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arXiv · 2311.14438

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

Andrew Graham·Vincent Pilloni·Joaquín Rodrigues Jacinto
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Abstract

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 Gouv\^{e}a 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.

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Andrew Graham, Vincent Pilloni, Joaquín Rodrigues Jacinto. 2023-11-24. p-adic interpolation of Gauss--Manin connections on nearly overconvergent modular forms and p-adic L-functions. https://doi.org/10.1112/s0010437x25102479

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