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

Matteo Longo; Paola Magrone; Eris Rocha Walchek

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

Number Theory 2026-05-05 v3

Authors: Matteo Longo , Paola Magrone , Eris Rocha Walchek

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.

Keywords

quaternionic modular forms ordinary families $p$-adic $L$-functions Serre--Tate expansion Hida family

Cite

@article{arxiv.2510.04301,
  title  = {On quaternionic ordinary families of modular forms and $p$-adic $L$-functions},
  author = {Matteo Longo and Paola Magrone and Eris Rocha Walchek},
  journal= {arXiv preprint arXiv:2510.04301},
  year   = {2026}
}

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38 pages

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

Abstract

Keywords

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