J. Aust. Math. Soc.
78 (2005), 37-57
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Multiplicities in Hayman's alternative
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Walter Bergweiler
Mathematisches Seminar
Christian-Albrechts-Universität zu Kiel
Ludewig-Meyn Str. 4
D-24098 Kiel
Germany
bergweiler@math.uni-kiel.de
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J. K. Langley
School of Mathematical Sciences
University of Nottingham
NG7 2RD
UK
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
 is transcendental and meromorphic in the plane
then either  takes every finite complex value infinitely
often or each derivative
 ,  , 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.
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