Densities in Fabry's theorem

TL;DR

This paper improves Fabry's theorem on power series singularities by replacing the maximum density condition with an interior density of Beurling--Malliavin type, offering a more refined criterion.

Contribution

It introduces a new density concept based on Beurling--Malliavin theory to enhance Fabry's theorem's applicability.

Findings

Replaces maximum density with interior Beurling--Malliavin density

Provides a more precise criterion for singularities of power series

Enhances the theoretical understanding of power series behavior

Abstract

Fabry's theorem on the singularities of power series is improved: the maximum density in the assumptions of this theorem is replaced by an interior density of Beurling--Malliavin type.