One a type of automorphic forms

The aim of the paper is to construct а $\Gamma$-automorphic form of weight $-2k$ for a given finitely generated Fuchsian group $\Gamma$ of the second kind. The construction heavily relies on important properties of the outer function introduced by Widom that have been established by the author. The $\Gamma$-automorphic form construced possesses the highest possible smoothness for the weight $-2k$.