Holomorphic curves with an infinite number of deficiencies
Nobushige Toda
Source: Proc. Japan Acad. Ser. A Math. Sci. Volume 80, Number 6
(2004), 90-95.
Abstract
For each positive integer $p$, there exists a holomorphic curve of order $p$ mean type with an infinite number of deficiencies, the sum of which to the a power is divergent, where $0 < a < 1/3$.
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Permanent link to this document: http://projecteuclid.org/euclid.pja/1116014783
Mathematical Reviews number (MathSciNet): MR2075448
Zentralblatt MATH identifier: 02138345
Digital Object Identifier: doi:10.3792/pjaa.80.90
References
Cartan, H.: Sur les combinaisons linéaires de $p$ fonctions holomorphes données. Mathematica 7, 5--31 (1933).
Chen, W.: Defect relations for degenerate meromorphic maps. Trans. Amer. Math. Soc., 319 (2), 499--515 (1990).
Mathematical Reviews (MathSciNet): MR1010882
Fujimoto, H.: Value Distribution Theory of the Gauss Map of Minimal Surfaces in $\mbox\boldmath $R$^m$. Aspects of Mathematics, E21, Friedr. Vieweg and Sohn, Braunschweig (1993).
Hayman, W. K.: Meromorphic Functions. Oxford Mathematical Monographs. Clarendon Press, Oxford (1964).
Mathematical Reviews (MathSciNet): MR164038
Nevanlinna, R.: Le théorème de Picard-Borel et la théorie des fonctions méromorphes. Gauthier-Villars, Paris (1929).
Nochka, E. I.: On the theory of meromorphic functions. Soviet Math. Dokl., 27-2, 377--381 (1983).
Mathematical Reviews (MathSciNet): MR701289
Weitsman, A.: A theorem of Nevanlinna deficiencies. Acta Math., 128, 41-52 (1972).
Mathematical Reviews (MathSciNet): MR387597
Weyl, H.: Meromorphic Functions and Analytic Curves. Annals of Mathematics Studies, no. 12, Princeton Univ. Press, Princeton, N.J. (1943).
Mathematical Reviews (MathSciNet): MR9057
Zentralblatt MATH: 0061.15302
Krutin, V. I.: On the magnitudes of the positive deviations and of the defects of entire curves of finite lower order. Math. USSR Izvestija, 13, 307--333 (1979).
Hussain, M.: The defects and deviations of entire curves. Teor. Funkcii. Funkcional. Anal. i Prilozen., 20, 161--171 (1974), (in Russian).
Mathematical Reviews (MathSciNet): MR379906
Savchuk, Ya. I.: Set of deficient vectors of integral curves. Ukrain. Mat. Zh., 35, 385--389 (1983), (in Russian); English Translation in Ukrain. Math. J., 35, 334--338 (1983).
Mathematical Reviews (MathSciNet): MR704345
Proceedings of the Japan Academy, Series A, Mathematical Sciences