华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (3): 61-70.

• 应用数学与基础数学 • 上一篇    下一篇

涉及微分多项式及例外函数的正规定则

王 雪1, 刘晓俊2, 陈巧玉3   

  1. 1. 阜阳师范学院~~数学系, 安徽~阜阳 236041; 2. 上海理工大学~~数学系, 上海 200093; 3. 华东师范大学~~数学系, 上海 200241
  • 收稿日期:2011-06-10 修回日期:2011-09-01 出版日期:2012-05-25 发布日期:2012-05-22

Normal criterion concerning differential polynomials and omitted functions

WANG Xue 1, LIU Xiao-jun 2, CHEN Qiao-yu 3   

  1. 1. Department of Mathematics, Fuyang Normal College, Fuyang Anhui 236041, China; 2. Department of Mathematics,University of Shanghai for Science and Technology, Shanghai 200093, China; 3. ,Department of Mathematics, East China Normal University, Shanghai 200241, China
  • Received:2011-06-10 Revised:2011-09-01 Online:2012-05-25 Published:2012-05-22

摘要: 证明了如下的结论: 设\,k2\,是一个正整数, F\,是区域\,D\,上的一族全纯函数, 其中每个函数的零点重级至少是\,k, h(z),a1(z),a2(z),ak(z)\,是\,D\,上的不恒为零的全纯函数. 假设下面的两个条件也成立:\,fF, (a) 在\,f(z)\,的零点处, f(z)\,的微分多项式的模小于\,h(z)\,的模; (b) f(z)\,的微分多项式不取\,h(z), 则\,F\,在\,D\,上正规.

关键词: 全纯函数, 微分多项式, 正规

Abstract: In this paper, we proved: Let k2 be a positive integer, F be a family of holomorphic functions, all of whose zeros have multiplicities at least k, and let h(z), a1(z), a2(z), , ak(z) are all nonequivalent to 0 on D. If for any  fF, the following two conditions are satisfied: (a)~f(z)=0|f(k)(z)+a1(z)f(k1)(z)++ak(z)f(z)|<|h(z)|; (b)~f(k)(z)+a1(z)f(k1)(z)++ak(z)f(z)h(z),~ where ~a1(z),a2(z),,ak(z) and f have no common zeros, then F is normal on D.

Key words: holomorphic function, differential polynomial, normal

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