On Fabry's Gap Theorem

TL;DR

This paper presents a more general gap theorem in complex analysis by combining Turán's and Szűsz's results, expanding the understanding of Fabry's gap theorem.

Contribution

It introduces a unified gap theorem that generalizes previous results by Turán and Szűsz in the context of Fabry's theorem.

Findings

New generalized gap theorem established

Broader conditions for gap theorems derived

Enhanced understanding of Fabry's gap theorem achieved

Abstract

By combining Tur\'an's proof of Fabry's gap theorem with a gap theorem of P. Sz\"usz we obtain a gap theorem which is more general then both these theorems.