关于无穷级亚纯函数

Abstract

Abstract:

By using Nevanlinna theory of the angular domain and the type function of characteristic T(r,f), we study the value distribution of meromorphic functions of infinite order, obtain the existences of Borel direction and Hayman direction of proximate order dealing with small functions, at the same time prove existences of T direction and Hayman-T direction dealing with small functions, from which we can easily deduce the existing results.

Key words: Meromorphic function, Type functon, Borel direction, Hayman direction, T direction, Hayman-T direction

CLC Number:

O174.55

Zhang Hongshen, Ge Yuli. On Meromorphic Functions of Infinite Order[J].Acta mathematica scientia,Series A, 2016, 36(4): 750-762.

Trendmd

References

[1] Hiong K L. Sur les fonctions entiéres et les fonctions méromorphes d'ordre infini. J de Math, 1935, 14: 233-308
[2] 李国平. 半纯函数的聚值线理论. 北京: 科学出版社, 1958 Li G P. The Cluster Value Line Theory of Meromorphic Functions (in Chinese). Beijing: Science Press, 1958
[3] 庄圻泰. 亚纯函数的奇异方向. 北京: 科学出版社, 1982 Zhuang Q T. The Singular Directions of Meromorphic Functions (in Chinese). Beijing: Science Press, 1982
[4] 张洪申, 孙道椿. 关于单位圆内代数体函数的Borel点. 数学物理学报, 2011, 31A(6): 1512-1520 Zhang H S, Sun D C. On Borel point of algebroid functios in the unit circle. Acta Mathematica Scientia, 2011, 31A(6): 1512-1520
[5] Hayman W K. Picard values of meromorphic functions and derivatives. Ann of Math, 1959, 70(2): 9-42
[6] Yang L. Meromorphic functions and their derivatives. J London Math Soc, 1982, 25(2): 288-296
[7] 顾永兴, 龚向宏. 关于Hayman方向. 中国科学, 1987, 10: 1019-1030 Gu Y X, Gong X H. On Hayman direction. Science in China, 1987, 10: 1019-1030
[8] 张庆彩. 关于亚纯函数的奇异方向. 数学学报, 1988, 31(6): 777-785 Zhang Q C. On the singular directions of meromorphic functions. Acta Mahematica Sinica (in Chinese), 1988, 31(6): 777-785
[9] Rossi J, Fenton P. Cercles de remplissage for entire functions. Bull London Math Soc, 1999, 31: 59-66
[10] Zheng J H. Value Distribution of Meromorphic Functions. Beijing: Springer and Tsinghua Univ Press, 2010
[11] Zheng J H, Wu N. Hayman-T directions of meromorphic functions. Taiwanese Journal of Mathematics, 2010, 14(6): 2219-2228
[12] Wu N, Zheng J H. T-and Hayman T-points of meromorphic functions for small functions in the unit disk. Acta Mathematica Scientia, 2012, 32 B(4): 1662-1674
[13] Hayman W K. Meromorphic Function. London: Oxford, 1964
[14] Goldberg A A, Ostrovskii I V. Value Distribution of Meromorphic Functions. Providence, RI: American Mathematical Society, 2008
[15] 杨乐. 值分布论及其新研究. 北京: 科学出版社, 1982 Yang L. The Value Distribution Theory and Its New Research (in Chinese). Beijing: Science Press, 1982
[16] 孙道椿. Nevanlinna方向的存在性定理. 数学年刊, 1986, 7A(2): 212-221 Sun D C. The existence theorem of the Nevanlinna directions Chinese (in Chinese). Annals of Math, 1986, 7A(2): 212-221
[17] Wu N, Xuan Z X. Hayman T directions of meromorphic functions in some angular domains. Bull of the Korean Math Soc, 2013, 52(1): 1-11
[18] 孔荫莹, 刘兴臻. 单位圆内亚纯函数的Nevanlinna不等式和相关的奇异半径. 数学年刊, 2014, 35A(3): 351-360 Kong Y Y, Liou X Z. Nevanlinna inequalities and singular radiuses of meromorphic functions in |z|<1. Annals of Math, 2014, 35A(3): 351-360
[19] 孔荫莹. 圆内拟亚纯映射关于型函数的奇异半径. 数学物理学报, 2010, 30A(6): 1640-1647 Kong Y Y. A singular radius of quasimeromorphic mappings on some type-functions in the unit disc. Acta Mathematica Scientia, 2010, 30A(6): 1640-1647
[20] 刘慧芳, 孙道椿. 具有公共小函数的代数体函数的唯一性. 数学物理学报, 2015, 35A(2): 274-281 Liou H F, Sun D C. Uniqueness of algebroid functions concerning small functions. Acta Mathematica Scientia, 2015, 35A(2): 274-281
[21] Chai F J, Gao Z S. The normality of algebroid multifunctios and their coefficient functions. 2015, 35B(1): 121-132

On Meromorphic Functions of Infinite Order

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Guo Xiaojing, Sun Daochun. Covering Surface Inequality on the Ring and Its Applications [J]. Acta Mathematica Scientia, 2018, 38(5): 833-841.
[2]	Deng Bingmao, Lei Chunlin, Fang Mingliang. Normality and Shared Function Concerning Differential Polynomials [J]. Acta mathematica scientia,Series A, 2018, 38(2): 222-230.
[3]	Yang Qi, Chen Wei, Yuan Wenjun. The Normal Family of Meromorphic Functions Concerning Zero Numbers [J]. Acta mathematica scientia,Series A, 2017, 37(4): 624-636.
[4]	Liu Aichao, Cui Yanyan, Liu Hao. The Distortion Estimation for Strongly Spirallike Mappings of Type α Along Unit Direction [J]. Acta mathematica scientia,Series A, 2017, 37(2): 239-247.
[5]	Wang Qiong, Chen Wei, Yuan Wenjun, Tian Honggen. Normality Criteria of Meromorphic Functions with Zero Numbers [J]. Acta mathematica scientia,Series A, 2017, 37(1): 7-17.
[6]	Xuan Zuxing, Xu Hongyan. Borel Directions and Uniqueness of Analytic Functions [J]. Acta mathematica scientia,Series A, 2016, 36(4): 740-749.
[7]	Zhang Shaohua, Liu Huifang, Sun Daochun. The Algebroid Functions with Given Borel Directions [J]. Acta mathematica scientia,Series A, 2016, 36(3): 401-412.
[8]	Yang Duanyang, Ye Yasheng. Normality Concerning Shared Functions [J]. Acta mathematica scientia,Series A, 2016, 36(3): 425-432.
[9]	Luo Jie, Lin Weichuan. Uniqueness Theorem of Meromorphic Functions with Non-Integer [J]. Acta mathematica scientia,Series A, 2016, 36(2): 244-253.
[10]	Zeng Juanjuan, Liu Huifang. Uniqueness of Meromorphic Functions Concerning Nonlinear Differential Polynomials Sharing a Polynomial [J]. Acta mathematica scientia,Series A, 2016, 36(2): 254-266.
[11]	Yang Pai. Quasinormal Criterion and Picard Type Theorem [J]. Acta mathematica scientia,Series A, 2015, 35(6): 1089-1105.
[12]	Zhao Lijuan. Normal Families of Meromorphic Functions and Multiple Values [J]. Acta mathematica scientia,Series A, 2015, 35(2): 256-263.
[13]	ZHANG Ke, WANG Jun. Complex Oscillation of Meromorphic Solutions of Some Difference Equations [J]. Acta mathematica scientia,Series A, 2015, 35(1): 218-224.
[14]	QI Xiao-Guang, YANG Lian-Zhong. Value Sharing for a Meromorphic Function with Its q-Shift Difference [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1372-1380.
[15]	LIU Dan, DENG Bing-Mao, YANG De-Gui. Valiron Quasi-Deficient of Meromorphic Functions [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1474-1480.