Uniqueness problem with truncated multiplicities in value distribution theory

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 decl...

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Bibliographic Details
Published inNagoya mathematical journal Vol. 152; pp. 131 - 152
Main Author Fujimoto, Hirotaka
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.12.1998
Duke University Press
Subjects
30D35
32H30
Online AccessGet full text
ISSN0027-7630
2152-6842
DOI10.1017/S0027763000006826

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Summary: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.
ISSN:0027-7630
2152-6842
DOI:10.1017/S0027763000006826