Analogues of the Bol operator for half-integral weight weakly holomorphic modular forms

TL;DR

This paper introduces an analogue of the Bol operator for half-integral weight weakly holomorphic modular forms, exploring its properties and connections within the theory of modular forms.

Contribution

It defines a new operator for half-integral weight forms and investigates its fundamental properties and relationships with existing mathematical objects.

Findings

Established the main properties of the analogue Bol operator.

Connected the operator with other structures in modular form theory.

Provided a framework for future research on half-integral weight modular forms.

Abstract

We define an analogue of the Bol operator on spaces of weakly holomorphic modular forms of half-integral weight. We establish its main properties and relation with other objects.