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Some Note on Exceptional Values of Meromorphic Functions

Published online by Cambridge University Press:  22 January 2016

Kikuji Matsumoto
Kikuji Matsumoto*
Affiliation:
Mathematical Institute, Nagoya University
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Let E be a totally-disconnected compact set in the z-plane and let Ω be its complement with respect to the extended z-plane. Then Ω is a domain and we can consider a single-valued meromorphic function w = f(z) on Ω which has a transcendental singularity at each point of E. Suppose that E is a null-set of the class W in the sense of Kametani [4] (the class NB in the sense of Ahlfors and Beurling [1]). Then the cluster set of f(z) at each transcendental singularity is the whole w-plane, and hence f(z) has an essential singularity at each point of E. We shall say that a value w is exceptional for f(z) at an essential singularity ζ ∈ E if there exists a neighborhood of ζ where the function f(z) does not take this value w.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 22 , June 1963 , pp. 189 - 201
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1963

References

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