Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-02-04T22:35:18.583Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks to the uniqueness problem of meromorphic maps into PN(C), II

Published online by Cambridge University Press:  22 January 2016

Hirotaka Fujimoto
Hirotaka Fujimoto*
Affiliation:
Nagoya University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [7], R. Nevanlinna gave the following uniqueness theorem of meromorphic functions as an improvement of a result of G. Pólya ([8]).

Theorem A. Let f, g be non-constant meromorphic functions on C. If there are five mutually distinct values a1, …, a5 such that f−1(ai = g−1(ai) (1 ≦ i ≦ 5), then f ≡ g.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 71 , November 1978 , pp. 25 - 41
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

[1] Borel, E., Sur les zéros des fonctions entières, Acta Math., 20 (1897), 357–396.CrossRefGoogle Scholar
[2] Cartan, H., Sur les zéros des combinaisons linéaires de p fonctions holomorphes. données, Mathematica, 7 (1933), 5–31.Google Scholar
[3] Fujimoto, H., On meromorphic maps into the complex projective space, J. Math. Soc. Japan, 26 (1974), 272–288.CrossRefGoogle Scholar
[4] Fujimoto, H., The uniqueness problem of meromorphic maps into the complex projective space, Nagoya Math. J., 58 (1975), 1–23.CrossRefGoogle Scholar
[5] Fujimoto, H., A uniqueness theorem of algebraically non-degenerate meromorphic maps into PN(C), Nagoya Math. J., 64 (1976), 117–147.CrossRefGoogle Scholar
[6] Fujimoto, H., Remarks to the uniqueness problem of meromorphic maps into PN(C), I, Nagoya Math. J., 71 (1978), 13–24.CrossRefGoogle Scholar
[7] Nevanlinna, R., Einige Eindeutigkeitssätze in der Theorie der meromorphen Funktionen, Acta Math., 48 (1926), 367–391.CrossRefGoogle Scholar
[8] Pólya, G., Bestimmung einer ganzen Funktionen endlichen Geschlechts durch viererlei Stellen, Math. Tidskrift, København, B. 1921, 16–21.Google Scholar