Normality and Montel's Theorem

TL;DR

This paper introduces a new normality criterion for families of meromorphic functions with zeros of certain multiplicities, extending Montel's classical normality test by involving shared holomorphic functions.

Contribution

It generalizes Montel's normality test by establishing a criterion based on shared holomorphic functions and zero multiplicities in meromorphic function families.

Findings

New normality criterion for meromorphic functions

Extension of Montel's normality test

Applicable to functions sharing holomorphic functions

Abstract

In this article, we prove a normality criterion for a family of meromorphic functions having zeros with some multiplicity which involves sharing of a holomorphic function by the members of the family. Our result generalizes Montel's normality test in a certain sense.