数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1441-1448.doi: 10.1016/S0252-9602(12)60113-1

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ON THE NEVANLINNA DIRECTION OF ALGEBROID FUNCTIONS

张洪中1|孙道椿2   

  1. 1.Department of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, China; 2.School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • 收稿日期:2010-11-04 修回日期:2011-03-29 出版日期:2012-07-20 发布日期:2012-07-20
  • 基金资助:

    The work is supported by NSFC (10471048) and NSF of Henan Province in China (112300410300).

ON THE NEVANLINNA DIRECTION OF ALGEBROID FUNCTIONS

 |ZHANG Hong-Shen1, SUN Dao-Chun2   

  1. 1.Department of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, China; 2.School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China
  • Received:2010-11-04 Revised:2011-03-29 Online:2012-07-20 Published:2012-07-20
  • Supported by:

    The work is supported by NSFC (10471048) and NSF of Henan Province in China (112300410300).

摘要:

In this paper, we prove that for an algebroid function w(z), the singular direction arg z φ0, satisfying that for arbitrary ε(0 < επ/2 ) and any given a α ∈C , lim r→∞n(r,φ0εφ0+ε, w=a)/log r= +∞ holds with at most 2v possible exceptional values of a, is the Nevanlinna direction of w(z).

关键词: algebroid function, Nevanlinna direction

Abstract:

In this paper, we prove that for an algebroid function w(z), the singular direction arg z φ0, satisfying that for arbitrary ε(0 < επ/2 ) and any given a α ∈C , lim r→∞n(r,φ0εφ0+ε, w=a)/log r= +∞ holds with at most 2v possible exceptional values of a, is the Nevanlinna direction of w(z).

中图分类号: 

  • 30D30