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arXiv · 2510.04301

On quaternionic ordinary families of modular forms and $p$-adic $L$-functions

Matteo Longo·Paola Magrone·Eris Rocha Walchek
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Abstract

We use Serre--Tate expansions of modular forms to construct power series attached to quaternionic ordinary families of modular forms. We associate to these power series a big $p$-adic $L$-function interpolating the $p$-adic $L$-functions constructed by Burungale and Magrone at classical specializations. A crucial ingredient is the generalization of some results of Ohta to the quaternionic setting.

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Matteo Longo, Paola Magrone, Eris Rocha Walchek. 2025-10-05. On quaternionic ordinary families of modular forms and $p$-adic $L$-functions. https://arxiv.org/abs/2510.04301

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