一类代数体函数的Montel定则

Montel Theorem of a Kind of Algebroidal Functions

区域D上的代数体函数族W={W_a(z):φ(z,w_a)=A_(k,a)(z)w_a^k+A_(0,a)(z)=0,α∈Λ}(Λ为一指标集).若W中每个代数体函数都不取a_1,a_2,a_3三个互异的复数(其中a_i^k≠a_j^k,i≠j,i,j=1,2,3.)或不取2k+1个互异的复数,则W在D内正规.

This paper prove a theorem on family of Algebroidal functions that if the range of each function W_a(z) in the family doesn't include 3 distinct complex numbers a_1,a_2,a_3(a_i^k≠a_j^k,i≠j,i;j=1,2,3) respectively or the range of any numbers in the family doesn't include 2k+1 distinct complex numbers,then the family is normal in its domain.