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ON FILLING DISCS IN THE STRONG BOREL DIRECTION OF ALGEBROID FUNCTION WITH FINITE ORDER

  • Huo, Yingying (SCHOOL OF MATHEMATICS GUANGDONG UNIVERSITY OF TECHNOLOGY) ;
  • Kong, Yinying (SCHOOL OF MATHEMATICS AND COMPUTATIONAL SCIENCE GUANGDONG UNIVERSITY OF BUSINESS STUDIES)
  • Received : 2009.04.13
  • Published : 2010.11.30

Abstract

Using Ahlfors' covering surface method, some properties on the strong Borel direction of algebroid function of finite order are obtained. The main object of this paper is to prove existence theorem of a strong Borel direction and the existence of filling discs in such direction which briefly extends some results of meromorphic function.

Keywords

algebroid function;strong Borel direction;Type-function;filling disc

References

  1. Z. S. Gao and D. C. Sun, The Borel directions of the largest type of algebroid functions, Chinese Ann. Math. Ser. A 18 (1997), no. 6, 701-710.
  2. W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
  3. Y. Z. He and X. Z. Xiao, Algebroid Function and Ordinary Differential Equation, Science Press, China, 1988(in Chinese).
  4. Y. Y. Kong, On filling discs in Borel radius of meromorphic mapping with finite order in the unit circle, J. Math. Anal. Appl. 344 (2008), no. 2, 1158-1164. https://doi.org/10.1016/j.jmaa.2008.04.010
  5. G. P. Li, The Theory on Cluster Line of Meormorphic Function, Wuhan University Press(in Chinese).
  6. Y. N. Lu and Y. X. Gu On the existence of Borel Direction for algebroid function, Chinese Sci. Bull 28 (1983), 264-266.
  7. A. Rauch, Extension de theoremes relatifs aux directions de Borel des functions meromorphes, J. Math. Pures Appl. 12 (1933), 109-171.
  8. H. Selberg, Uber die wertverteilung der algebroiden funktionen, Math. Z. 31 (1930), no. 1, 709-728. https://doi.org/10.1007/BF01246442
  9. D. C. Sun, Filling discs of algebroid function, Chinese Ann. Math. Ser. A 16 (1995), no. 2, 238-243.
  10. D. C. Sun and Y. Y. Kong, The growth of algebroidal function, J. Math. Anal. Appl. 332 (2007), no. 1, 542-550. https://doi.org/10.1016/j.jmaa.2006.10.031
  11. N. Toda, Sur les directions de Julia et de Borel des fonctions algebroides, Nagoya Math. J. 34 (1969), 1-23. https://doi.org/10.1017/S0027763000024429
  12. G. Valiron, Sur la derivee des fonctions algebrodes, Bull. Soc. Math. France 59 (1931), 17-39.
  13. G. Valiron, Sur les direction de Borel des fonctions algebrodes meromorphes d'order infini, C. R. Acad. Sci. Paris 206 (1938), 735-737.
  14. L. Yang, Value distribution theory and its new reasearch, Science Press, Beijing, 1982, in Chinese; Springer-Verlag, 1993, in English.

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  2. The Filling Discs Dealing with Multiple Values of an Algebroid Function in the Unit Disc vol.2012, 2012, https://doi.org/10.1155/2012/426302
  3. Distribution of branch points of some algebroid functions in the unit disc vol.62, pp.4, 2017, https://doi.org/10.1080/17476933.2016.1234460
  4. General algebroid function and its application vol.36, pp.1, 2016, https://doi.org/10.1016/S0252-9602(15)30095-3