涉及零点的非零亚纯函数的正规性

Normality Concerning Zero Numbers of Zero-free Meromorphic Functions

文章主要讨论了涉及零点个数的非零亚纯函数的正规性.主要结果为:设F是区域D内的一族亚纯函数,k,q(≥1)是两个正整数.若对任意的f∈F,f(z)≠0且(f^(k))~q-1至多有q(k+1)-1个不同的零点(不计重数),则F在D内正规.这个结果推广了常建明的结论.

In this paper,we discussed the normality concerning zero numbers of zero-free meromorphic functions and obtained the following results:Let Fbe a family of meromorphic functions in a domain D,let k,q(≥1),be two positive integers.If,for each function f ∈ F,f(z)≠0,(f^(k))~q-1,has at most q(k+1)-1distinct zeros(ignoring multiplicity)in D,then is normal in D.This extends the result of Chang[8].