# 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.

## Key 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 $\omega > 0$.

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Source: https://tomesphere.com/paper/1905.12288