零点位于直线上的亚纯函数的正规定则

摘要

The normality of meromorphic functions whose zeros distribute on some straight lines was discussed and it is proved:let F be a family of meromorphic functions on a unit disk D,all of whose poles have multiplicity at least m,where m≥3 is an integer.If there exists M≥0,such that for each f∈F,all zeros of f distribute on a straight line,f′(z)≠1 ,z∈D and f= 0 f′ ≤M, then F is normal on D.%讨论了亚纯函数的零点分布在直线上的亚纯函数的正规性，得到：设犉是定义在单位圆盘D上的亚纯函数族，若存在M≥0，使得对于犉中任意的亚纯函数f满足f的零点分布在一直线上，其极点重级m≥3（m∈瓕＋），且f′（狕）不取1，当f取值0时，f′（狕）的模不大于M，则犉在区域D内是正规的。