Kodai Mathematical Journal

Some extensions of the four values theorem of Nevanlinna-Gundersen

Duc Quang Si

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Abstract

Nevanlinna showed that two distinct non-constant meromorphic functions on C must be linked by a Möbius transformation if they have the same inverse images counted with multiplicities for four distinct values. Later on, Gundersen generalized the result of Nevanlinna to the case where two meromorphic functions share two values ignoring multiplicity and share other two values with counting multiplicities. In this paper, we will extend the results of Nevanlinna-Gundersen to the case of two holomorphic mappings into Pn(C) sharing (n + 1) hyperplanes ignoring multiplicity and other (n + 1) hyperplanes with multiplicities counted to level 2 or (n + 1).

Article information

Source
Kodai Math. J., Volume 36, Number 3 (2013), 579-595.

Dates
First available in Project Euclid: 5 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1383660699

Digital Object Identifier
doi:10.2996/kmj/1383660699

Mathematical Reviews number (MathSciNet)
MR3161557

Zentralblatt MATH identifier
1279.32017

Citation

Si, Duc Quang. Some extensions of the four values theorem of Nevanlinna-Gundersen. Kodai Math. J. 36 (2013), no. 3, 579--595. doi:10.2996/kmj/1383660699. https://projecteuclid.org/euclid.kmj/1383660699


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