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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| Published in | Nagoya mathematical journal Vol. 152; pp. 131 - 152 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.12.1998
Duke University Press |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0027-7630 2152-6842 |
| DOI | 10.1017/S0027763000006826 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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 P N (ℂ). We show that there are at most two nondegenerate meromorphic maps of ℂ n into P N (ℂ) which share 3 N + 1 hyperplanes in general position counted with multiplicities truncated by two. We also give some degeneracy theorems of meromorphic maps into P N (ℂ) and discuss some other related subjects. |
| Author | Fujimoto, Hirotaka |
| Author_xml | – sequence: 1 givenname: Hirotaka surname: Fujimoto fullname: Fujimoto, Hirotaka email: fujimoto@kappa.s.kanazawa-u.ac.jp organization: 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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| Cites_doi | 10.1090/conm/025/730045 10.1017/S0027763000016676 10.5186/aasfm.1988.1307 10.4099/math1924.11.233 10.2996/kmj/1138039844 10.2969/jmsj/04530481 10.1007/BF02565342 10.2748/tmj/1178228497 10.1017/S0027763000021607 10.1017/S002776300001758X 10.2140/pjm.1988.135.323 |
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| Copyright | Copyright © Editorial Board of Nagoya Mathematical Journal 1998 Copyright 1998 Editorial Board, Nagoya Mathematical Journal |
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| References | Steinmetz (S0027763000006826_ref13) 1988; 13 Cartan (S0027763000006826_ref1) 1929; 188 Shiftman (S0027763000006826_ref11) 1983; 981 S0027763000006826_ref3 S0027763000006826_ref2 S0027763000006826_ref5 S0027763000006826_ref4 S0027763000006826_ref12 S0027763000006826_ref10 S0027763000006826_ref7 S0027763000006826_ref6 S0027763000006826_ref9 S0027763000006826_ref8 |
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| Title | Uniqueness problem with truncated multiplicities in value distribution theory |
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