J. Aust. Math. Soc.
78 (2005), 3757

Multiplicities in Hayman's alternative

Walter Bergweiler
Mathematisches Seminar
ChristianAlbrechtsUniversität zu Kiel
LudewigMeyn Str. 4
D24098 Kiel
Germany
bergweiler@math.unikiel.de



J. K. Langley
School of Mathematical Sciences
University of Nottingham
NG7 2RD
UK
jkl@maths.nott.ac.uk



Abstract

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 nonzero 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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