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

2023/11/24 by A.J. Graham, Graham, Andrew, Vincent Pilloni +3
Mathematics · #11F33 #11F67 #11F77 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2311.14438

openalex publication_date 2023/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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 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.

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