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On Exceptional Values of Meromorphic Functions with the Set of Singularities of Capacity Zero1)

Published online by Cambridge University Press:  22 January 2016

Kikuji Matsumoto
Kikuji Matsumoto*
Affiliation:
Department of Mathematics, Hiroshima University
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Extract

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Let E be a compact set in the z-plane and let Ω be its complement with respect to the extended z-plane. Suppose that E is of capacity zero. Then Ω is a domain and we shall consider a single-valued meromorphic function w = f(z) on Ω which has an essential singularity at each point of E. We shall say that a value w is exceptional for f(z) at a point ζ ∈ E if there exists a neighborhood of C where the function f(z) does not take this value w.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 18 , April 1961 , pp. 171 - 191
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1961

Footnotes

1)

In this paper, capacity is always logarithmic.

References

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