Annales AcademiŠ Scientiarum FennicŠ
Mathematica
Volumen 37, 2012, 301-307

A PROPERTY OF THE DERIVATIVE OF AN ENTIRE FUNCTION

Walter Bergweiler and Alexandre Eremenko

Christian-Albrechts-Universitńt zu Kiel, Mathematisches Seminar
Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany; bergweiler 'at' math.uni-kiel.de

Purdue University, Department of Mathematics
West Lafayette, IN 47907, U.S.A.; eremenko 'at' math.purdue.edu

Abstract. We prove that the derivative of a non-linear entire function is unbounded on the preimage of an unbounded set.

2010 Mathematics Subject Classification: Primary 30D30.

Key words: Entire function, normal family.

Reference to this article: W. Bergweiler and A. Eremenko: A property of the derivative of an entire function. Ann. Acad. Sci. Fenn. Math. 37 (2012), 301-307.

Full document as PDF file

doi:10.5186/aasfm.2012.3721

Copyright © 2012 by Academia Scientiarum Fennica