• DOI:10.1007/S00013-002-8303-4
• Corpus ID: 123068490

Julia directions of meromorphic functions and their derivatives

@article{Sauer2002JuliaDO,
  title={Julia directions of meromorphic functions and their derivatives},
  author={Andreas Sauer},
  journal={Archiv der Mathematik},
  year={2002},
  volume={79},
  pages={182-187},
  url={https://api.semanticscholar.org/CorpusID:123068490}
}

• A. Sauer
• Published 1 September 2002
• Mathematics
• Archiv der Mathematik

Abstract. We prove that if a transcendental meromorphic function has no Julia direction and is bounded on a path to $ \infty $ then there is a common Julia direction for all derivatives. Related statements are obtained under the assumption that f is $ o(\sqrt{\mid z \mid}) $ or $ O(\sqrt{\mid z \mid}) $ on a path to $ \infty $. Further we disprove a conjecture of Frank and Wang by means of a counterexample.  

Abstract. We prove that if a transcendental meromorphic function has no Julia direction and is bounded on a path to
$ \infty $ then there is a common Julia direction for all derivatives. Related statements are obtained under the assumption that f is
$ o(\sqrt{\mid z \mid}) $ or
$ O(\sqrt{\mid z \mid}) $ on a path to
$ \infty $. Further we disprove a conjecture of Frank and Wang by means of a counterexample.