微分多项式分担集合的亚纯函数正规定则

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

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．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.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/Abstract

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

中图分类号:

O17452

曾翠萍;雷春林;李淑龙;杨德贵. 微分多项式分担集合的亚纯函数正规定则[J]. 中山大学学报自然科学版, 2011, 50(4): 17-22.

ZENG Cuiping;LEI Chunlin;LI Shulong;YANG Degui. Normality and Shared Sets Concerning Differential Polynomial[J]. , 2011, 50(4): 17-22.