Zeros of differential polynomials in real meromorphic functions

Details Zeros of differential polynomials in real meromorphic functions Zeros of differential polynomials in real meromorphic functions

2004-07-12

arxiv.org/abs/math/0407207v1

Proc. Edinburgh Math. Soc. (2005) 48 1-15

Mathematics

Complex Variables

18 pages

Scientific paper

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.

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