亚纯函数与其微分多项式的分担函数与正规族

设${\cal F}$为开平面内的区域$D$上的亚纯函数族, ${\cal F}$中任何函数$f(z)\in{\cal F}$, $f$的零点竽数至少为$k+1$.对于$D$内不等于零的解析函数$a(z)$.若$f(z)$与其微分多项式$D(f)$ IM分担$a(z)$,本文不仅得到${\cal F}$在$D$上正规, 而且得到相应于正规函数的结果.

Normality Family and Shared Functions by Meromorphic Functions and Its Differential Polynomials

In this paper, we obtain the following normal criterion: Let ${\cal F}$ be a family of meromorphic functions in domain $D\subset {\bf C}$, all of whose zeros have multiplicity $k+1$ at least. If there exist holomorphic functions $a(z)$ not vanishing on $D$, such that for every function $f(z)\in{\cal F}$, $f(z)$ shares $a(z)$ IM with $L(f)$ on $D$, then ${\cal F}$ is normal on $D$, where $L(f)$ is linear differential polynomials of $f(z)$ with holomorphic coefficients, and $k$ is some positive numbers. We also proved coressponding results on normal functions.