关于亚纯代数体函数的奇异方向

Abstract

Abstract:

Let w(z) be a meromorphic algebroidal function for |z|<+∞. If lim_r →∞lg T(r, w)/lg r =0, lim_r →∞lg T(r, w)/lg lg r =+∞, then there exists a direction arg z=θ₀ such that, for any N>0, ∑_i1/(lg|z_i(a; ?(θ₀, δ))|)^N=+∞, with 2 v possible exceptions for a. If lim_r _→∞T(r, w)/lg^Kr =+∞, lim_r _→∞lg T(r, w)/lg lg r =M, then there exists a direction arg z=θ₀ such that ∑_i1/lg|z_i(a; ?(θ₀, δ))|)^σ=∞ (σ=M-2 or σ=M-2-ε), with 2 v possible exceptions for a. For meromorphic functions, these singular directions have not been studied yet.

Key words: Meromorphic algebroidal function, Singular direction

CLC Number:

30D30

ZHANG Hong-Shen. On Singular Directions of |Meromorphic Algebroidal Functions[J].Acta mathematica scientia,Series A, 2009, 29(6): 1642-1650.

Trendmd

References

[1] Lu Yinian. On the Borel directions of meromorphic algebroidal function. Science in China(in Chinese), 1981, A(6): 675--680

[2] Lu Yinian, Gu Yongxing. On the existence of Borel directions of meromorphic algebroidal function. Chinese Science Bulletin(in Chinese), 1983, 3(5): 264--266

[3] Lu Qian, Gu Yongxing. On Nevanlinna directions of algebroid functions. Acta Mathematica Scientia, 2005, 25B(2): 367--375

[4] Sun Daochun. The existence theorem of the Nevanlinna directions. Chinese Annals of Mathematics(in Chinese), 1986, 7A(2): 212--221

[5] Gao Zongshen, Sun Daochun. On the maximum type Borel direction of meromorphic algebroidal function. Chinese Annals of Mathematics(in Chinese), 1997, 18A(6): 701--710

[6] Zhang Hongshen, Sun Daochun. Fill-up discs of quasi-meromorphic mappings. Acta Mathematica Scientia(in Chinese), 2004, 24A(6): 758--766

[7] Toda N. Sur les directions de Julia et de Borel des functions algebroides. Nagoya Math Journal, 1969, 34: 1--23

[8] Lu Yinian. Julia directions of meromorphic function and meromorphic algebroidal function. Acta Mathematica Sinica(in Chinese), 1984, 27(6): 367--373

[9] Tsuji M. Potential Theory in Modern Function Theory. Tokyo: Maruzen, 1959: 271--275

[10] Yang Le. Value Distribution and New Studies. Beijing: Academic Press(in Chinese), 1982: 96--97

[11] He Yuzan, Xiao Xiuzhi. Algebroidal Function and Ordinary Differential Equations. Beijing: Academic Press(in Chinese), 1988: 5--26

[12] GanHuilin, Sun Daochun. The maximality Borel direction of zero order algebroidal function. Acta Mathematica Scientia(in Chinese), 2005, 25A(5): 673--677

[13] 张洪申. 单位圆内拟亚纯映射的重值.数学物理学报, 2006, 26A(3): 337--342

[14] 吴昭君, 孙道椿. 代数体函数的一类新的奇异方向.数学物理学报, 2008, 28A(5): 879--885

[15] 柳学坤, 吴昭君. 关于亚纯函数的奇异方向. 数学物理学报, 2007, 27A(5): 590--597

On Singular Directions of |Meromorphic Algebroidal Functions

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 2

Metrics

Comments

Recommended 10

[1]	LI Xiao-Min, YI Hong-Xun. UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE NONLINEAR DIFFERENTIAL POLYNOMIALS SHARE ONE VALUE OR HAVE THE SAME FIXED POINTS IN AN ANGULAR DOMAIN [J]. Acta mathematica scientia,Series A, 2014, 34(3): 593-609.
[2]	PAN Biao. Sharing Values and Angular Value Distribution of an Integral Function [J]. Acta mathematica scientia,Series A, 2005, 25(7): 945-951.