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Zeros of differences of meromorphic functions

Published online by Cambridge University Press:  12 February 2007

WALTER BERGWEILER  and
J. K. LANGLEY
WALTER BERGWEILER
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. e-mail: jkl@maths.nott.ac.uk
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Abstract

Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = Δf(z) = f(z + 1) − f(z). A number of results are proved concerning the existence of zeros of g(z) or g(z)/f(z), in terms of the growth and the poles of f. The results may be viewed as discrete analogues of existing theorems on the zeros of f' and f'/f.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 1 , January 2007 , pp. 133 - 147
Copyright
Copyright © Cambridge Philosophical Society 2007

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