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Perfect Picard Set of Positive Capacity

Published online by Cambridge University Press:  22 January 2016

Kikuji Matsumoto
Kikuji Matsumoto*
Affiliation:
Mathematical Institute, Nagoya University
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In our previous paper [1], we proved that any Cantor set E with successive ratios ξn satisfying the condition

is a Picard set, that is, each single-valued meromorphic function with E as the set of essential singularities takes on every value infinitely often in any neighborhood of each singularity with the possible exception of two values.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 29 , March 1967 , pp. 51 - 56
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1967

References

[1] Matsumoto, K.: Existence of perfect Picard sets, Nagoya Math. J. 27 (1966), 213–222.Google Scholar