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The Distribution of Finite Values of Meromorphic Functions with Deficient Poles

Published online by Cambridge University Press:  12 December 2008

G. F. Kendall
G. F. Kendall
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
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Abstract

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A result is presented giving conditions on a set of open discs in the complex plane that ensure that a transcendental meromorphic function with Nevanlinna deficient poles omits at most one finite value outside the set of discs. This improves a previous result of Langley, and goes some way towards closing a gap between Langley's result and a theorem of Toppila in which the omitted values considered may include ∞

Keywords

exceptional setvalue distributionPicard setNevanlinna theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 3 , October 2008 , pp. 697 - 709
Copyright
Copyright © Edinburgh Mathematical Society 2008