代数体函数的一个正规定则

A New Normal Criterion of Algebroidal Function

本文运用覆盖曲面,克服了代数体函数多值性及分支点的困难,建立了一个代数体函数的正规定理,并证明了:对分支点分担的代数体函数族,若族中每个函数都不取互异的三个复数,则此函数族正规。

In this paper, a new normal criterion of algebroidal function is proposed by applying the main theorems on covering surface, which overcomes some difficulties caused by the multivaluedness and bifurcation points. We continue to prove the fol- lowing result: For those algebroidal function families where the bifurcation points are shared, the function family is normal, if every function in these families is not equal to three different values.