Proceedings of the Japan Academy, Series A, Mathematical Sciences

Unicity theorems for meromorphic functions

Wei-Ran Lü and Hong-Xun Yi

Full-text: Open access

Abstract

In this paper, we deal with the problem of uniqueness of meromorphic functions sharing three values, and prove some results which are improvements and extensions of many known theorems. Examples are provided to show that the results in this paper are sharp.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 7 (2002), 152-156.

Dates
First available in Project Euclid: 23 May 2006

Permanent link to this document
https://projecteuclid.org/euclid.pja/1148392640

Digital Object Identifier
doi:10.3792/pjaa.78.152

Mathematical Reviews number (MathSciNet)
MR1930222

Zentralblatt MATH identifier
1026.30033

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory
Secondary: 30D30: Meromorphic functions, general theory 30D20: Entire functions, general theory

Keywords
Nevanlinna theory shared value unicity theorem

Citation

Yi, Hong-Xun; Lü, Wei-Ran. Unicity theorems for meromorphic functions. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 7, 152--156. doi:10.3792/pjaa.78.152. https://projecteuclid.org/euclid.pja/1148392640


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References

  • Hayman, W. K.: Meromorphic Functions. Clarendon Press, Oxford (1964).
  • Yi, H.-X., and Yang, C.-C.: Uniqueness Theory of Meromorphic Functions. Pure and Applied Math. Monographs, no. 32, Science Press, Beijing (1995).
  • Gundensen, G. G.: Meromorphic functions that share three or four values. J. London Math. Soc., 20, 457–466 (1979).
  • Nevanlinna, R.: Le Th$\acute{e}$or$\grave{e}$me de Picard-Borel et la Th$\acute{e}$orie des Fonctions M$\acute{e}$romorphes. Gauthiers-Villars, Paris (1929).
  • Ozawa, M.: Unicity theorems for entire functions. J. d'Anal. Math., 30, 411–420 (1976).
  • Ueda, H.: Unicity theorems for meromorphic or entire functions II. Kodai Math. J., 3, 26–36 (1983).
  • Ueda, H.: On the zero-one-pole set of a meromorphic function II. Kodai Math. J., 13, 134–142 (1990).
  • Brosch, G.: Eindeutigkeitssätze für meromorphe funktionen. Thesis, Technical University of Aachen (1989).
  • Mues, E.: Shared value problems for meromorphic functions. Value Distribution Theory and Complex Differential Equations (Joensuu, 1994), Joensuun Yliop. Luonnont. Julk., vol. 35, pp. 17–43 (1995).
  • Yi, H.-X.: Meromorphic functions that share three values. Chin. Ann. Math., 9A, 433–440 (1988).
  • Yi, H.-X.: Meromorphic functions that share two or three values. Kodai Math. J., 13, 363–372 (1990).
  • Yi, H.-X.: Unicity theorems for meromorphic functions that share three values. Kodai Math. J., 18, 300–314 (1995).
  • Yi, H.-X.: Meromorphic functions that share three values. BHKMS, 2, 55–64 (1998).
  • Li, P., and Yang, C.-C.: On the characteristics of meromorphic functions that share three values CM. J. Math. Anal. Appl., 220, 132–145 (1998).
  • Zhang, Q.-C.: Meromorphic functions sharing three values. Indian J. Pure Appl. Math., 30, 667–682 (1999). \end{