Non-real zeros of derivatives of real meromorphic functions

TL;DR

This paper characterizes specific real meromorphic functions of finite order based on the distribution of zeros of the functions and their derivatives, focusing on the finiteness of real and non-real zeros.

Contribution

It provides a complete classification of real meromorphic functions with finitely many zeros in their derivatives under certain conditions, advancing understanding of zero distribution.

Findings

Classifies all such functions with finitely many zeros in derivatives

Establishes conditions linking zeros of functions and derivatives

Identifies functions with specific zero distribution patterns

Abstract

The main result of the paper determines all real meromorphic functions of finite order in the plane for which the first derivative has finitely many zeros, while the function itself and one of its higher derivatives have finitely many non-real zeros.