涉及分担值的正规定则
Some Normal Criteria Concerning Shared Values

设 $\mathcal F$是区域 $D$上的一个亚纯函数族, $k\ (\geq 2)$是一个正整数, $b$是一个非零复数, $M$是一个正数. 若对任意给定的 $f \in \mathcal F$, $f$的零点重数至少为$k$, 且$f(z)=0 \Rightarrow |f^{(k)}(z)| \leq M$. 如果对任意给定的函数 $f,g \in \mathcal F$, $L(f)$与 $L(g)$的零点都为重零点, 且$L(f)$与$L(g)$在区域 $D$内分担$b$, 则$\mathcal F$在区域 $D$内正规.
Let $\mathcal F$ be a family of meromorphic functions in a domain $D$, $k\ (\geq 2)$ a positive integer, $b$ a nonzero finite complex number, and $M$ a positive number. Suppose that for each $f \in \mathcal F$, all zeros of $f$ have multiplicity at least $k$, and $f(z)=0 \Rightarrow |f^{(k)}(z)| \leq M$. If for each pair $f,g \in \mathcal F$, all zeros of $L(f)$ and $L(g)$ are multiple, and $L(f)$ and $L(g)$ share $b$ in $D$, then $\mathcal F$ is normal in $D$.