Proceedings of the Japan Academy, Series A, Mathematical Sciences

On the order of holomorphic curves with maximal deficiency sum, II

Nobushige Toda

Full-text: Open access

Abstract

In this paper we consider the order of holomorphic curves with maximal deficiency sum in the complex plane. The purpose of this paper is to weaken the condition treated in the paper [9]. As a special case we obtain the result in [9].

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 94, Number 7 (2018), 71-75.

Dates
First available in Project Euclid: 17 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.pja/1531814465

Digital Object Identifier
doi:10.3792/pjaa.94.71

Mathematical Reviews number (MathSciNet)
MR3829184

Subjects
Primary: 32H30: Value distribution theory in higher dimensions {For function- theoretic properties, see 32A22}
Secondary: 30D35: Distribution of values, Nevanlinna theory

Keywords
Holomorphic curve order meromorphic function

Citation

Toda, Nobushige. On the order of holomorphic curves with maximal deficiency sum, II. Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 7, 71--75. doi:10.3792/pjaa.94.71. https://projecteuclid.org/euclid.pja/1531814465


Export citation

References

  • E. Cartan, Sur les zéros des combinaisons linéaires de $p$ fonctions holomorphes donées, Mathematica (Cluj) 7 (1933), 5–31.
  • H. Fujimoto, Value distribution theory of the Gauss map of minimal surfaces in $\mathbf{R}^{m}$, Aspects of Mathematics, E21, Friedr. Vieweg & Sohn, Braunschweig, 1993.
  • W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
  • R. Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Chelsea Publishing Co., New York, 1974.
  • E. I. Nochka, On the theory of meromorphic curves, Dokl. Akad. Nauk SSSR 269 (1983), no. 3, 547–552.
  • N. Toda, Sur une relation entre la croissance et le nombre de valeurs déficientes de fonctions algébroïdes ou de systèmes, Kōdai Math. Sem. Rep. 22 (1970), 114–121.
  • N. Toda, Sur la croissance de fonctions algébroïdes à valeurs déficientes, Kōdai Math. Sem. Rep. 22 (1970), 324–337.
  • N. Toda, An extension of the derivative of meromorphic functions to holomorphic curves, Proc. Japan Acad. Ser. A Math. Sci. 70 (1994), no. 6, 159–163.
  • N. Toda, On the order of holomorphic curves with maximal deficiency sum, Kodai Math. J. 18 (1995), no. 3, 451–474.
  • N. Toda, On the second fundamental inequality for holomorphic curves, Bull. Nagoya Inst. Tech. 50 (1998), 123–135.
  • N. Toda, On the deficiency of holomorphic curves with maximal deficiency sum. II, in Progress in Analysis, Vol. I, II (Berlin, 2001), 287–300, World Sci. Publ., River Edge, NJ, 2003.
  • N. Toda, A generalization of Nochka weight function, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 9–10, 170–175.
  • N. Toda, On the truncated defect relation for holomorphic curves, Kodai Math. J. 32 (2009), no. 2, 352–389.
  • H. Weyl, Meromorphic Functions and Analytic Curves, Annals of Mathematics Studies, 12, Princeton University Press, Princeton, NJ, 1943.