On Quasi-Modular Forms, Almost Holomorphic Modular Forms, and the Vector-Valued Modular Forms of Shimura

TL;DR

This paper broadens the understanding of quasi-modular and almost holomorphic modular forms by connecting them to vector-valued modular forms with symmetric power representations and establishing a general structure theorem.

Contribution

It extends the relation between quasi-modular and modular forms to a wider class and relates them to vector-valued forms, proving a comprehensive structure theorem.

Findings

Extended the relation to a broader class of functions

Connected quasi-modular forms to vector-valued modular forms

Proved a general structure theorem for these forms

Abstract

We extend the relation between quasi-modular forms and modular forms to a wider class of functions. We then relate both forms to vector-valued modular forms with symmetric power representations, and prove a general structure theorem for these vector-valued forms.