Acta mathematica scientia, Series B >
ON THE NEVANLINNA DIRECTION OF ALGEBROID FUNCTIONS
Received date: 2010-11-04
Revised date: 2011-03-29
Online published: 2012-07-20
Supported by
The work is supported by NSFC (10471048) and NSF of Henan Province in China (112300410300).
In this paper, we prove that for an algebroid function w(z), the singular direction arg z = φ0, satisfying that for arbitrary ε(0 < ε < π/2 ) and any given a α ∈C , lim r→∞n(r,φ0−ε, φ0+ε, w=a)/log r= +∞ holds with at most 2v possible exceptional values of a, is the Nevanlinna direction of w(z).
ZHANG Hong-Shen , SUN Dao-Chun . ON THE NEVANLINNA DIRECTION OF ALGEBROID FUNCTIONS[J]. Acta mathematica scientia, Series B, 2012 , 32(4) : 1441 -1448 . DOI: 10.1016/S0252-9602(12)60113-1
[1] Lv Yinian, Zhang Guanghou. On the Nevanlinna direction of a meromorphic function. Science in China, 1983, A(3): 215–224
[2] Sun Daochun. The existence theorem of the Nevanlinna directions. Chin Ann Math, 1986, 7A(2): 212–221
[3] Lin Qun. The Nevanlinna direction of meromorphic functions. Chin Ann Math, 1986, 7A(6): 670–675
[4] Zhang Qingde. On the Nevanlinna direction and Borel direction of a meromorphic function. Acta Math Sinica, 1986, 29(4): 550–554
[5] Lv Yinian, Sun Daochun. The Nevanlinna direction and the Julia direction. Chin Ann Math, 1992, 13A(3): 289–295
[6] Lu Qian, Gu Yongxing. On Nevanlinna direction of algebroid functions. Acta Math Sci, 2005, 25B(2): 367–375
[7] Xuan Zuxing, Gao Zongsheng. On the Nevanlinna direction of an algebroid function dealing with multiple values. J Math Anal Appl, 2007, 325: 268–278
[8] Lv Yinian. The Julia direction of meromorphic functions and algebroid functions. Acta Math Sinica, 1984, 27(6): 367–373
[9] He Yuzan, Xiao Xiuzhi. Algebroid Functions and Ordinary Differential Equations. Beijing: Science Press, 1988
[10] Zhuang Qitai. The Singular Directions of Meromorphic Functions. Beijing: Science Press, 1982
[11] Sun Daochun. Main theorem on covering surfaces. Acta Math Sci, 1994, 14(2): 213–225
[12] Y. Tumura. Quelques applications de la th´eorie de M. Ahlfors. Japan J Math, 1942-1943, 18: 303–322
[13] Gao Zongsheng, Sun Daochun. On the Borel direction of the largest type of algebroid functions. Chin Ann Math, 1997, 18A(6): 701–710
[14] Zhang Hongshen, Sun Daochun. Fill-up Discs of Quasi-meromorphic Mappings. Acta Math Sci, 2004, 24A(6): 758–766
/
| 〈 |
|
〉 |