Zeros of differential polynomials in real meromorphic functions
Complex Variables
2008-08-08 v1
Abstract
We show that for a real transcendental meromorphic function f, the differential polynomial f'+f^m with m > 4 has infinitely many non-real zeros. Similar results are obtained for differential polynomials f'f^m-1. We specially investigate the case of meromorphic functions with finitely many poles. We show by examples the precision of our results. One of our main tools is the Fatou theorem from complex dynamics.
Cite
@article{arxiv.math/0407207,
title = {Zeros of differential polynomials in real meromorphic functions},
author = {W. Bergweiler and A. Eremenko and J. Langley},
journal= {arXiv preprint arXiv:math/0407207},
year = {2008}
}
Comments
18 pages