Browse > Article
http://dx.doi.org/10.4134/BKMS.2010.47.6.1213

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)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.6, 2010 , pp. 1213-1224 More about this Journal
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;
Citations & Related Records

Times Cited By Web Of Science : 2  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
연도 인용수 순위
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.   DOI   ScienceOn
5 G. P. Li, The Theory on Cluster Line of Meormorphic Function, Wuhan University Press(in Chinese).
6 D. C. Sun, Filling discs of algebroid function, Chinese Ann. Math. Ser. A 16 (1995), no. 2, 238-243.
7 Y. N. Lu and Y. X. Gu On the existence of Borel Direction for algebroid function, Chinese Sci. Bull 28 (1983), 264-266.
8 A. Rauch, Extension de theoremes relatifs aux directions de Borel des functions meromorphes, J. Math. Pures Appl. 12 (1933), 109-171.
9 H. Selberg, Uber die wertverteilung der algebroiden funktionen, Math. Z. 31 (1930), no. 1, 709-728.   DOI
10 D. C. Sun and Y. Y. Kong, The growth of algebroidal function, J. Math. Anal. Appl. 332 (2007), no. 1, 542-550.   DOI   ScienceOn
11 N. Toda, Sur les directions de Julia et de Borel des fonctions algebroides, Nagoya Math. J. 34 (1969), 1-23.   DOI
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.