Differential operators on modular forms (mod p)

TL;DR

This paper surveys recent developments in constructing differential operators on modular forms mod p and explores their impact on associated Galois representations, advancing understanding in modular forms and number theory.

Contribution

It introduces a framework for analyzing how differential operators affect mod p Galois representations attached to Hecke eigenforms, highlighting new insights.

Findings

Construction methods for differential operators on modular forms mod p

Framework for analyzing effects on Galois representations

Implications for understanding modular forms and Galois actions

Abstract

We give a survey of recent work on the construction of differential operators on various types of modular forms (mod p). We also discuss a framework for determining the effect of such operators on the mod p Galois representations attached to Hecke eigenforms.