亚纯函数微分多项式的一个正规定则  

A Normality Criterion for Meromorphic Functions with One of Its Differential Polynomials

作　　者：张兆迎[1] 鲍文竹[1] 

机构地区：[1]成都信息工程学院数学学院,四川成都610225

出　　处：《成都信息工程学院学报》2010年第2期218-220,共3页Journal of Chengdu University of Information Technology

摘　　要：证明了下面两个定理:(1)设n,k≥2为正整数,a为有穷非零复数,F为区域D上的亚纯函数族,F中任一函数的零点重级至少为k.f,g∈F,fLn(f)与gLn(g)I M分担a.则F在D上正规,其中L(f)为f(k)+a1f(k-1)+…+akf,这里a1,…,ak为常数.(2)设n,k为正整数,且n≥2,a为有穷非零复数,F为区域D上的亚纯函数族,F中任一函数的零点重级至少为k,且fLn(f(z))=a能够推出|f(k)(z)|≤A,其中A为正数,则F在区域D上正规.In this paper we obtain the following results： 1. Take positive integers n, k ≥2. Let F be a family of meromorphic functions defined on a domain D in the complex plane, such that each f∈F has only zeros of multiplicity at least k. For each pair f,g in F, fLn（f） and gLn（g） share a non-zero complex value a ignoring multiplicity. Then F is normal on D, where L（f） is defined f（k） ＋ alf（k-1） ＋ ... ＋ akf, in which al,…,ak are constants. 2.Take positive integers n and k with n≥2 and take a non-zero complex number a. Let F be a family of meromorphic functions in the plane domain D such that each f∈F has only zeros of multiplicity at least k. For each element f of F,if fLn（f（z）） = a implies If（k）（z）≤A for a positive number A, then F is normal in D.

关 键 词：基础数学 函数论 亚纯函数 正规族 分担值 

分 类 号：O174.52[理学—数学]