04-8   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Walter Bergweiler, Alexandre Eremenko, James Langley:

Zeros of differential polynomials in real meromorphic functions

We show that for a real transcendental meromorphic function f, the differential polynomial f' + fm with m > 4 has infinitely many non-real zeros. Similar results are obtained for differential polynomials f'fm-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.

Electronic Print: Front for the Mathematics ArXiv

Mathematics Subject Classification (1991): 30D30

Bibliographical note: Proc. Edinburgh Math. Soc. 48, 279-293 (2005)

Mail an Jens Burmeister
[Thu Feb 19 18:56:36 2009]