Families of Differential Operators for Overconvergent Hilbert Modular Forms

TL;DR

This paper develops differential operators for overconvergent Hilbert modular forms, extending existing theories and enabling applications such as p-adic L-functions for CM fields.

Contribution

It introduces a new family of differential operators for overconvergent Hilbert modular forms by interpolating the Gauss--Manin connection.

Findings

Constructed differential operators for overconvergent Hilbert modular forms.

Connected the operators to p-adic L-functions of CM fields.

Extended previous work on modular and Siegel modular forms.

Abstract

We construct differential operators for families of overconvergent Hilbert modular forms by interpolating the Gauss--Manin connection on strict neighborhoods of the ordinary locus. This is related to work done by Harron and Xiao and by Andreatta and Iovita in the case of modular forms and by Zheng Liu for Siegel modular forms. It has applications in particular to $p$-adic $L$-functions of CM fields.