On $m$--fold Holomorphic Differentials and Modular Forms

TL;DR

This paper explores the relationship between m/2-holomorphic differentials and cuspidal modular forms for Fuchsian groups, providing detailed analysis of Wronskians and their divisors.

Contribution

It establishes a connection between holomorphic differentials and modular forms, and offers an in-depth study of Wronskians in this context.

Findings

Characterization of m/2-holomorphic differentials via modular forms

Analysis of Wronskians and their divisors

Insights into the structure of cuspidal modular forms

Abstract

Let $\Gamma$ be the Fuchsian group of the first kind. For an even integer $m\ge 4$, we study $m/2$-holomorphic differentials in terms of space of (holomorphic) cuspidal modular forms $S_m(\Gamma)$. We also give in depth study of Wronskians of cuspidal modular forms and their divisors.