Edrei和Fuchs亏量椭圆定理的推广

EXTENSION OF EDREI AND FUCHS'S ELLIPTIC THEOREM FOR DIFFICIENCIES

设 f 是由以下不可约方程所定义的 n 值代数体函数:ψ(z,f)≡A_0(z)f^n+A_1(z)f^(n-1)+…+A_(n-1)(z)f+A_n(z)=0,(1)这里,A_0(z),A_1(z),…,A_n(z)是没有公共零点的整函数,设 f_1,f_2,…,f_n 是 f 的 n 个分支。

Edrei and Fuchs have proved the famous elliptic theorem.Shea has also proved the el-liptic theorem for Valiron deficiency.Adding the condition“zero is not a Valiron deficientvalue for A_0(z)”Sato extended the above results to n-valued algebroid functions.In this paper,that condition is removed and n mutually distinct complex constants a_j are extended to nmutually distinct meromorphic function (?)_j which satisfy T(r,(?)_j)=0(T(r,f))(j=1,2,…,n).These results complte the elliptic theorems for Nevanlinna deficiency and Valiron deficiency.