代数体函数的正规定理

详细信息

NORMAL THEOREM OF ALGEBROIDAL FUNCTIONS

摘要: 运用覆盖曲面的几何方法,证明了代数体函数族一个正规定理:设 $F$ 为区\\域 $D$ 内的一族 $k$ 值代数体函数,且 $F$ 的分支点是孤立的.若对 $\forall p\in D,$ 总存在一\\个含于 $D$ 内的邻域 $U(p),$ 使得在 $U(p)$ 内,对每个 $f_{t}\in F$ 存在三个判别的复数 $a_{t1},\\a_{t2},a_{t3},$ 满足 $\sum\limits_{i=1}^{3}\overline{n}(U(p),a_{ti},f_{t})\leq 1,$ 则 $F$ 在 $D$ 内正规.
- 代数体函数 /
- 分支点 /
- 覆盖曲面 /
- 正规族
Abstract: By applying the main theorems on covering surface, a new normal criterion of algebroidal function was obtained. Let $F$ be a family of $k$ -valued algebroidal functions in a domain $D$ of sphere $V,$ and the branch points of $F$ be isolated. If for all $p\in D,$ there is a neighborhood $U(p)$ such that for every $f_{t}\in F,$ there exist three different complex values $a_{t1},a_{t2},a_{t3}$ satisfying $\sum\limits_{i=1}^{3}\overline{n}(U(p),a_{ti},f_{t})\leq 1,$ then $F$ is normal in $D.$
- algebroidal function /
- branch point /
- covering surface /
- normal family