Cauchy Integral Formula for Fuchsian Groups. II

TL;DR

This paper generalizes a classical complex analysis result, extending the Cauchy integral formula to derivatives within the context of Fuchsian groups, broadening its applicability in geometric function theory.

Contribution

It introduces a generalized version of Hasumi's Direct Cauchy Theorem for derivatives in the setting of Fuchsian groups, advancing the theoretical framework.

Findings

Proves a generalized Cauchy integral formula for derivatives in Fuchsian groups

Extends classical complex analysis results to a broader geometric setting

Provides new tools for studying automorphic functions

Abstract

We prove a generalization of the Hasumi's Direct Cauchy Theorem property for the derivatives (Theorem 2.2).