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Entire functions with two radially distributed values

Published online by Cambridge University Press:  04 April 2017

WALTER BERGWEILER ,
ALEXANDRE EREMENKO  and
AIMO HINKKANEN
WALTER BERGWEILER
Affiliation:
Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig–Meyn–Str. 4, 24098 Kiel, Germany. e-mail: bergweiler@math.uni-kiel.de
ALEXANDRE EREMENKO
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, U.S.A. e-mail: eremenko@math.purdue.edu
AIMO HINKKANEN
Affiliation:
Department of Mathematics, University of Illinois at Urbana–Champaign, 1409 W. Green St., Urbana, IL 61801, U.S.A. e-mail: aimo@math.uiuc.edu
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Abstract

We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are constructed, using the Stokes phenomenon for second order linear differential equations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 165 , Issue 1 , July 2018 , pp. 93 - 108
Copyright
Copyright © Cambridge Philosophical Society 2017 

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