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Existence of normal meromorphic functions with a perfect set as the set of essential singularities

Published online by Cambridge University Press:  22 January 2016

Toshiko Kurokawa
Toshiko Kurokawa*
Affiliation:
Department of Mathematics, Faculty of Education, Mie University, Tsu 514, Japan
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We are interested in whether there is a Cantor set E admitting no exceptionally ramified or normal meromorphic functions with E as the set of essential singularities. As for an exceptionally ramified meromorphic function, we [2] have recently given the following result.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 103 , October 1986 , pp. 29 - 37
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

[1] Constantinescu, C. , Einige Anwendungen des hyperbolischen Masses, Math. Nachr., 15 (1956), 155–172.CrossRefGoogle Scholar
[2] Kurokawa, T., Exceptionally ramified meromorphic functions with a non-enumerable set of essential singularities, Nagoya Math. J., 88 (1982), 133–154.Google Scholar
[3] Lehto, O. and Virtanen, K. I., Boundary behaviour and normal meromorphic functions, Acta Math., 97 (1957), 47–65.Google Scholar
[4] Toppila, S., Linear Picard sets for entire functions, Ann. Acad. Sci. Fennicae, Ser. I, 1 (1975), 111–123.Google Scholar