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Multiplicities in Hayman's alternative

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

Walter Bergwelier  and
J. K. Langley
Walter Bergwelier
Affiliation:
Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Ludewig-Meyn Str. 4, D-24098 Kiel, Germany e-mail: bergweiler@math.uni-kiel.de
J. K. Langley
Affiliation:
School of Mathematical Sciences, University of Nottingham, NG7 2RD, UK e-mail: jkl@maths.nott.ac.uk
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Abstract

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In 1959 Hayman proved an inequality from which it follows that if f is transcendental and meromorphic in the plane then either f takes every finite complex value infinitely often or each derivative f(k), k ≥1, takes every finite non-zero value infinitely often. We investigate the extent to which these values may be ramified, and we establish a generalization of Hayman's inequality in which multiplicities are not taken into account.

MSC classification

Secondary: 30D35: Distribution of values, Nevanlinna theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 78 , Issue 1 , February 2005 , pp. 37 - 58
Copyright
Copyright © Australian Mathematical Society 2005

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