Linear differential polynomials in zero-free meromorphic functions

TL;DR

This paper characterizes meromorphic functions with finitely many zeros whose higher-order linear differential polynomials also have finitely many zeros, expanding understanding of zero distribution in complex analysis.

Contribution

It provides a complete classification of such meromorphic functions and their differential polynomials, a novel result in the study of zero distribution.

Findings

Classification of meromorphic functions with finitely many zeros

Conditions under which differential polynomials have finitely many zeros

Extension of zero distribution theory in complex analysis

Abstract

The paper determines all meromorphic functions with finitely many zeros in the plane having the property that a linear differential polynomial in the function, of order at least 3 and with rational functions as coefficients, also has finitely many zeros.