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Exceptionally ramified meromorphic functions with a non-enumerable set ofessential singularities

Published online by Cambridge University Press:  22 January 2016

Toshiko Kurokawa
Toshiko Kurokawa*
Affiliation:
Department of Mathematics, Mie University, Kamihama, Tsu-shi, 514, Japan
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In the complex function theory, Picard’s Great Theorem plays an essential and important role. It is well-known as generalizations of this theorem that in a neighborhood of an isolated essential singularity, a meromorphic function cannot be exceptionally ramified (see W. Gross [2]) and that even it cannot be normal (see O. Lehto and K. I. Virtanen [7]). We are therefore interested in the behaviour of meromorphic functions with non-isolated essential singularities as well as in generalizations of the Gross’ result. Several approaches in this direction have been made by G. af Hällström [3], S. Kametani [4], K. Noshiro [13], K. Matsumoto [8], [9], [10], [11], [12], S. Toppila [15], etc..

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 88 , December 1982 , pp. 133 - 154
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

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