华东师范大学学报(自然科学版) ›› 2003, Vol. 2003 ›› Issue (4): 12-18.

• 论文 • 上一篇    下一篇

分担值和正规族

章文华1,2;庞学诚1   

  1. 1.华东师范大学 数学系,上海 200062;2.华东理工大学 数学系,上海 200237
  • 收稿日期:2001-12-19 修回日期:2002-01-21 出版日期:2003-12-25 发布日期:2003-12-25

Shared Values and Normality

ZHANG Wen-hua1,2,PANG Xue-cheng1   

  1. 1.Department of Mathematics,East China Normal University, Shanghai 20062,China 2.Department of Mathematics, East China University of Science and Technology,Shanghai 200237,China
  • Received:2001-12-19 Revised:2002-01-21 Online:2003-12-25 Published:2003-12-25

摘要： 设∮是单位圆盘⊿上的一族亚纯函数族,a和b是两个不同的有限复数,如果对于∮中的每一个函数f, f和f(k)在⊿上分担a和b,而且f(z)-a的零点重级≧k,其中k≧3是一个正整数,则∮在⊿上正规.

关键词: 亚纯函数, 分担值, 正规族, 亚纯函数, 分担值, 正规族

Abstract:

Let ∮be a family of meromorphic function on the unit disc ⊿ and let a and b be distinct values. If for every f∈∮, f and f(k) share a and b on ⊿ and the zero of f(z)-a are of multiplicity ≧k,where k≧3 be a positive integer,then ∮ is normal on ⊿.

Key words: shared values, normal family, meromorphic function, shared values, normal family