零点分布在直线上的亚纯函数的正规定则

Normal Criterion of Meromorphic Functions Whose Zeros Distribute on a Certain Straight Line

对零点分布在给定直线上的亚纯函数的正规性进行了讨论,设F是定义在单位圆盘D上的亚纯函数族,若存在M≥0,使得对于任意f∈F满足:f(z)=0 =〉f′≤M z m;f(z)的零点分布在一条给定直线上;f(z)的极点重数至少为3;f′(z)≠z m,则F在区域D上正规.

The normality of meromorphic functions whose zeros distribute on a certain straight lines was discussed and obtained：let Fbe a family of meromorphic functions on the unit disc D,if there exists M ≥0,such that for each f∈F,f（z）=0 =〉f′ ≤M z m,all zeros of f（z）distribute on a certain straight line,all of whose poles have multiplicity at least 3,and f′（z）≠z m,z∈D,then Fis normal on D.