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.
On quaternionic ordinary families of modular forms and p-adic L-functions
Longo M.;Magrone P.;
2026
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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