代数体函数族的Marty正规定则

The Marty Criterion for Families of Algebroid Functions

Marty正规定则在亚纯函数的正规族理论中具有十分重要的作用,然而该定则对代数体函数是不成立的.本文首先深入考察了亚纯函数的Marty正规定则,然后基于Ahlfors覆盖曲面理论,在形式上对该正规定则进行了推广,最后证明了此推广形式的Marty正规定则对一类代数体函数也是成立的.

The Marty criterion for meromorphic functions plays an important role in normal family theory.However,this normal criterion can not hold in algebroid functions.We genalize Marty criterion for meromorphic functions to a new form firstly,by using Ahlfors covering surfaces theory,and then we prove that the condition of this new Marty criterion is a necessary and sufficient condition for normal families of algebroid functions.