涉及零点与多项式的无零点亚纯函数族的正规性

Normality Concerning Zero Numbers and Polynomial of Zero-Free Meromorphic Functions

主要讨论了涉及零点与多项式的无零点亚纯函数族的正规性.主要结果为:设F是区域D内的一族亚纯函数,k,q为正整数,h(z)为区域D内不恒为0的全纯函数.若对任意的f∈F,f(z)≠0,且(f^(k)(z))~q-(h(z))~q至多有q(k+1)-1个不同的零点(不计重数),那么F在D内正规.

In this paper,we have discussed the normality concerning zero numbers and polynomial of zerofree meromorphic functions and obtained the following result：Let F be a family of zero-free meromorphic functions in a domain D,let h（z）be a holomophic functions in D,and let k,qbe two positive integers.If,for each function f∈F,f（z）≠0,（f^k（z））^q-（h（z））^q has at most q（k＋1）-1 distinct zeros（ignoring multiplicity）in D,then Fis normal in D.