T- AND HAYMAN T-POINTS OF MEROMORPHIC FUNCTIONS FOR SMALL FUNCTIONS IN THE UNIT DISK

doi:10.1016/S0252-9602(12)60132-5

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1662-1674.doi: 10.1016/S0252-9602(12)60132-5

T- AND HAYMAN T-POINTS OF MEROMORPHIC FUNCTIONS FOR SMALL FUNCTIONS IN THE UNIT DISK

吴楠¹|郑建华²

1.Department of Mathematics, School of Science, China University of Mining and Technology (Beijing)|2.Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

收稿日期:2009-02-24 修回日期:2011-02-22 出版日期:2012-07-20 发布日期:2012-07-20
基金资助:
The work is supported by the NSF of China(10871108).

T- AND HAYMAN T-POINTS OF MEROMORPHIC FUNCTIONS FOR SMALL FUNCTIONS IN THE UNIT DISK

WU Nan¹, ZHENG Jian-Hua²

1.Department of Mathematics, School of Science, China University of Mining and Technology (Beijing)|2.Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China

Received:2009-02-24 Revised:2011-02-22 Online:2012-07-20 Published:2012-07-20
Supported by:
The work is supported by the NSF of China(10871108).

摘要/Abstract

摘要：

In this article, we consider the singular points of meromorphic functions in the unit disk. We prove the second fundamental theorem for the Ahlfors-Shimizu's charac-teristic in the unit disk in terms of Nevanlinna theory in the angular domains, and obtain the existence of T-points and Hayman T-points dealing with small functions as target.

关键词: meromorphic functions, small functions, T-points, Hayman T-points, second fundamental theorem

Abstract:

Key words: meromorphic functions, small functions, T-points, Hayman T-points, second fundamental theorem

中图分类号:

30D10

吴楠, 郑建华. T- AND HAYMAN T-POINTS OF MEROMORPHIC FUNCTIONS FOR SMALL FUNCTIONS IN THE UNIT DISK[J]. 数学物理学报(英文版), 2012, 32(4): 1662-1674.

WU Nan, ZHENG Jian-Hua. T- AND HAYMAN T-POINTS OF MEROMORPHIC FUNCTIONS FOR SMALL FUNCTIONS IN THE UNIT DISK[J]. Acta mathematica scientia,Series B, 2012, 32(4): 1662-1674.

参考文献

[1] Goldberg A A, Ostrovskii I V. Value Distribution of Meromorphic Functions. Translations of Mathematical Monographs 236. American Mathematical Society, 2008

[2] Guo H, Zheng J H, Ng T W. On a new singular direction of meromorphic functions. Bull Austral Math Soc, 2004, 69: 277–287

[3] Gu Y X, Gong X H. On Hayman directions (in Chinese). Sci in China Ser A Math, 1987, 10: 1019–1030

[4] Han R S, Gu Y X. Distribution of arguments of meromorphic functions in the unit disk (in Chinese). J Chongqing Univ, 1999, 22: 120–125

[5] Hayman W K, Miles J. On the growth of a meromorphic function and its derivatives. Complex Variables, 1989, 12: 245–260

[6] Nevanlinna R. Le theoreme de Picard-Borel et la theorie des fonctions meromorphes. Paris, 1929

[7] Sun D C, Zhang X L. The fill-up disk in the unit disk and its application (in Chinese). Acta Math Sinica, 1992, 35(2): 279–285

[8] Tsuji M. Potential theory in modern function theory. Tokyo: Maruzen Co LTD, 1959

[9] Wang F Z. A result of the values distribution for meromorphic functions in |z| < 1 (in Chinese). Pure and Applied Math, 1995, 11: 121–126

[10] Wu G R, Pan B. On common Borel points of a meromorphic function and its differential polynomial in the unit circle (in Chinese). Acta Math Sci, 2000, 20: 540–546

[11] Wu Z J, Tian H G. The singular points of meromorphic mappings in the unit disk (in Chinese). J Xinjiang Nor Univ, 2006, 25(2): 9–12

[12] Yang L. Value Distribution and New Research. Berlin: Springer-Verlag, 1993

[13] Zhang H K, Xiao Z C. The T points of meromorphic functions in the unit disk. Chin Quart J Math, 2008, 23(1): 156–158

[14] Zheng J H. Value Distribution of Meromorphic Functions. Beijing: Springer and Tsinghua Univ Press, 2010

[15] Zheng J H. On transcentental meromorphic functions with radially distributed values. Sci in China Ser A Math, 2004, 47(3): 401–406

[16] Zheng J H. On value distribution of meromorphic functions with respect to arguments I. Complex Variables and Elliptic Equations, 2011, 56: 271–298

T- AND HAYMAN T-POINTS OF MEROMORPHIC FUNCTIONS FOR SMALL FUNCTIONS IN THE UNIT DISK

T- AND HAYMAN T-POINTS OF MEROMORPHIC FUNCTIONS FOR SMALL FUNCTIONS IN THE UNIT DISK

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