Advertisement

Archiv der Mathematik

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

Julia directions of meromorphic functions and their derivatives

  • A. Sauer

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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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.deDE

Personalised recommendations