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Uniqueness problem with truncated multiplicities in value distribution theory

Published online by Cambridge University Press:  22 January 2016

Hirotaka Fujimoto
Hirotaka Fujimoto*
Affiliation:
Department of Mathematics, Faculty of Science, Kanazawa University, Kakuma-machi, Kanazawa, 920-11, Japan, fujimoto@kappa.s.kanazawa-u.ac.jp
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Abstract.

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In 1929, H. Cartan declared that there are at most two meromorphic functions on ℂ which share four values without multiplicities, which is incorrect but affirmative if they share four values counted with multiplicities truncated by two. In this paper, we generalize such a restricted H. Cartan’s declaration to the case of maps into PN (ℂ). We show that there are at most two nondegenerate meromorphic maps of ℂn into PN(ℂ) which share 3N + 1 hyperplanes in general position counted with multiplicities truncated by two. We also give some degeneracy theorems of meromorphic maps into PN (ℂ) and discuss some other related subjects.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 152 , December 1998 , pp. 131 - 152
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1998

References

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