Overconvergent family of Siegel-Hilbert modular forms

TL;DR

This paper constructs one-parameter families of overconvergent Siegel-Hilbert modular forms, enabling the study of classical forms within a rigid analytic framework and showing how families of forms vary with weights.

Contribution

It introduces a method to construct overconvergent families of Siegel-Hilbert modular forms and demonstrates their accumulation properties around classical forms.

Findings

Existence of one-parameter families of overconvergent forms

Accumulation of classical points at the center of the family

Framework for studying variation of Siegel-Hilbert modular forms

Abstract

We construct one parameter families of overconvergent Siegel-Hilbert modular forms. In particular, for any classical Siegel-Hilbert modular eigenform one can find a rigid analytic disc centered at this point, on which an infinite family of classical points with varying weights accumulates at the center.