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ON T DIRECTION OF ALGEBROID FUNCTION DEALING WITH MULTIPLE VALUES

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  01 August 2008

ZHAOJUN WU  and
DAOCHUN SUN
ZHAOJUN WU*
Affiliation:
Department of Mathematics, Xianning University, Xianning, Hubei 437100, PR China (email: [email protected])
DAOCHUN SUN
Affiliation:
School of Mathematic, South China Normal University, Guangzhou, 510631, PR China (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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Using Ahlfors’ theory of covering surfaces, we prove the existence theorem for the T direction for algebroid functions dealing with multiple values which extends the results proved by Guo, Zheng and Ng and answers a question by Wang, Giao and the present authors.

Keywords

algebroid functionT directionmultiple values

MSC classification

Secondary: 30D30: Meromorphic functions, general theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 1 , August 2008 , pp. 147 - 156
Copyright
Copyright © 2008 Australian Mathematical Society

Footnotes

The first author was supported in part by Xianning University grants KT0623, KZ0629 and by NSF grant 10471048. The second author was supported in part by NSF grant 10471048.

References

[1]Guo, H., Zheng, J. H. and Ng, T. W., ‘On a new singular direction of meromorphic functions’, Bull. Austral. Math. Soc. 69 (2004), 277–287.Google Scholar
[2]He, Y. Z. and Xiao, X. Z., Algebroid Function and Ordinary Differential Equation (Science Press, Beijing, 1988).Google Scholar
[3]Lü, Y. N. and Gu, Y.-X., ‘On the existence of Borel direction for algebroid function’, Kexue Tongbao Math. 28 (1983), 264–266.Google Scholar
[4]Sun, D. C., ‘On the existence of Nevanlinna direction’, Chinese Ann. Math. Ser. A 7 (1986), 212–221 (in Chinese).Google Scholar
[5]Toda, N., ‘Sur les directions de Julia et de Borel des fonctions algebroides’, Nagoya Math. J. 34 (1969), 1–23.CrossRefGoogle Scholar
[6]Valiron, G., ‘Sur la dérivée des fonctions algébroïdes’, Bull. Soc. Math. France 59 (1931), 17–39.CrossRefGoogle Scholar
[7]Valiron, G., ‘Sur les direction de Borel des fonctions algebroïdes meromorphes d’ordre infini’, C. R. Acad. Sci. Paris 206 (1938), 735–737.Google Scholar
[8]Wang, S. M. and Gao, Z. S., ‘On a new singular direction of algebroid functions’, Bull. Austral. Math. Soc. 75 (2007), 459–468.CrossRefGoogle Scholar
[9]Wu, Z. J., ‘On T direction of algebroidal functions’, J. Math. Kyoto Univ. 47 (2007), 767–779.Google Scholar
[10]Wu, Z. J. and Sun, D. C., ‘On the existence of T direction of meromorphic function concerning multiple values’, Kodai Math. J. 31 (2008), 133–149.Google Scholar
[11]Yang, L., Value Distribution Theory and its New Research (Science Press, Beijing, 1982) (in Chinese); (Springer, Berlin, 1993) (in English).Google Scholar
[12]Zhang, S. H. and Sun, D. C., ‘On the singular direction of algebroid function’, Southeast Asian Bull. Math. 30 (2006), 1179–1189.Google Scholar
[13]Zheng, J. H., ‘On transcendental meromorphic functions with radially distributed values’, Sci. China Ser. A 47 (2004), 401–416.CrossRefGoogle Scholar
[14]Xuan, Z.-X., ‘On the existence of T-direction of algebroid functions: a problem of J. H. Zheng’, J. Math. Anal. Appl. 34 (2008), 540–547.Google Scholar