Higher Schwarzian, quasimodular forms and equivariant functions

Abstract

The Schwarzian derivative plays a fundamental role in complex analysis, differential equations, and modular forms. In this paper, we investigate its higher-order generalizations, known as higher Schwarzians, and their connections to quasimodular forms and equivariant functions. We prove that a meromorphic function is equivariant if and only if its higher Schwarzians are quasimodular forms of prescribed weight and depth, thereby extending classical results and linking projective differential operators to the structure of modular and quasimodular forms.

A new paper around the ideas of the withrawn paper will be submitted to arxiv. It contains many new developments so that it is not a mere replacement