中山大学学报自然科学版 ›› 2011, Vol. 50 ›› Issue (4): 17-22.

• 研究论文 • 上一篇    下一篇

微分多项式分担集合的亚纯函数正规定则

曾翠萍1,雷春林2,李淑龙3,杨德贵2

  

  1. (1.广东金融学院应用数学系,广东 广州 510521;2.华南农业大学理学院,广东 广州 510642;3.南方医科大学生物工程学院,广东 广州 510515)
  • 收稿日期:2010-07-02 修回日期:1900-01-01 出版日期:2011-07-25 发布日期:2011-07-25
  • 通讯作者: 杨德贵

Normality and Shared Sets Concerning Differential Polynomial

ZENG Cuiping1,LEI Chunlin2,LI Shulong3,YANG Degui2   

  1. (1.Department of Mathematics, Guangdong University of Finance, Guangzhou 510521, China;2.Department of Mathematics, South China Agricultural University, Guangzhou 510642, China;3.School of Biomedical Engineering,Southern Medical University,Guangzhou 510515, China)
  • Received:2010-07-02 Revised:1900-01-01 Online:2011-07-25 Published:2011-07-25

摘要: 研究涉及微分多项式分担集合的亚纯函数的正规性问题。设k≥2是正整数,F为区域D的一族亚纯函数, 其所有零点重级至少为k;a,b和c是复数,且a≠b,c≠0。如果对于F中的任意一对函数f(z)和g(z),有f与g分担c, 且L(f)与L(g)分担集合S={a,b}, 则F在D内正规。

关键词: 正规族, 亚纯函数, 分担集合, 微分多项式

Abstract: Normality and shared sets concerning differential polynomial are studied. Let k≥2 be a positive integer, and let F be a family of meromorphic functions defined in D, all of whose zeros have multiplicity at least k, and let a,b and c be complex numbers such that a≠b,c≠0. If for each pair of functions f,g∈F, f and g share c, L(f)and L(g)share the set S={a,b}in D ,then F is normal in D.

Key words: normal families, meromorphic function, shared sets, differential polynomial

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