On $m$--fold Holomorphic Differentials and 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.