亚纯函数的分担值与正规族(英文)

Share Values and Normality of Meromorphic Functions

假设F是区域D■C的一亚纯函数族.设k(≥2)是一个正整数,且a,b,c,d是4个相互判别的有限复数并满足c≠0,d≠a,c≠b.对每个函数f∈F,如果f-a所有的零点的重级不小于k,且f(k)=b当且仅当f=a,f(k)=c当f=d,那么F在D内正规.

Let F be a family of meromorphic functions in a domain D lohtain in C, let k ≥ 2 be a positive integer, and a, b, c, d be four finite complex numbers such that c ≠ 0, d ≠a, c ≠b. If for every f∈ F, all zeros of f- a have multiplicity at least k,and f^（k） = b if and only if f= a,and f = d whenever f^（k） = c,then F is normal in D.