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<p>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 <i>p</i>-adic <i>L</i>-function interpolating the <i>p</i>-adic <i>L</i>-functions constructed by Burungale and Magrone at classical specializations. A crucial ingredient is the generalization of some results of Ohta to the quaternionic setting.</p>

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

  • 期刊论文

  • 发表日期：

    2026年6月20日

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  • Matteo Longo,
  • Paola Magrone,
  • Eris R. Walchek

摘要

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.