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Archiv der Mathematik

, Volume 79, Issue 3, pp 182–187 | Cite as

Julia directions of meromorphic functions and their derivatives

  • A. Sauer
Article

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.

Keywords

Meromorphic Function Related Statement Transcendental Meromorphic Function Julia Direction 

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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • A. Sauer
    • 1
  1. 1.Fachbereich Mathematik, Gerhard-Mercator-Universität Duisburg, Lotharstr. 65, D-46047 Duisburg, Germany,¶ e-mail: sauer@math.uni-duisburg.deGermany

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