Partial Classicality of Hilbert Modular Forms

TL;DR

This paper proves a partial classicality theorem for overconvergent Hilbert modular forms over totally real fields, showing that small slope forms are partially classical under certain weight conditions using analytic continuation.

Contribution

It introduces a new partial classicality theorem for overconvergent Hilbert modular forms based on slope and weight conditions, employing analytic continuation methods.

Findings

Small slope overconvergent forms are partially classical.

Classicality depends on specific weight conditions.

Analytic continuation is effective for proving partial classicality.

Abstract

Let F be a totally real field and p a rational prime unramified in F. We prove a partial classicality theorem for overconvergent Hilbert modular forms: when the slope is small compared to certain but not all weights, an overconvergent form is partially classical. We use the method of analytic continuation.