A generalization of a theorem of Poincaré
A generalization of a theorem of Poincaré
Let $G$ be a finitely generated Fuchsian group of the first kind. Let $\varphi$ be a cusp form, and $f$ a solution to ${\theta _2}f = \varphi$, where ${\theta _2}$ is the Schwarzian derivative. Then for every $A \in G$ there is a Möbius transformation $\chi (A)$ such that $f …