Non-real zeros of linear differential polynomials in real meromorphic functions

TL;DR

This paper proves that for certain real entire functions of infinite order with only real zeros, the differential polynomial f'' + ωf has infinitely many non-real zeros, revealing complex zero distribution properties.

Contribution

It establishes a new result on the non-real zeros of linear differential polynomials for a class of real entire functions of infinite order.

Findings

f'' + ωf has infinitely many non-real zeros for specified functions

The result applies to functions with only real zeros and infinite order

Provides insight into zero distribution of differential polynomials

Abstract

It is shown that if $f$ or $1/f$ is a real entire function of infinite order of growth, with only real zeros, then $f''+\omega f$ has infinitely many non-real zeros for any $\omega > 0$.