关于代数体函数的微分多项式(英文)

ON DIFFERENTIAL POLYNOMIALS OF ALGEBROID FUNCTIONS

本文证明 v值代数函数的微分多项式是一 λ值 (1≤ λ≤v)代数体函数 ,即 v值代数体函数w=w(z)的微分多项式 p(w)可以被如下方程确定 :[ελ(z) pλ +ελ-1 (z) pλ-1 +… +ε0 (z) ] k =0这里ε0 (z) ,ε1 (z) ,… ,ελ(z)为整函数且无公共零点 ,λ和 k为正整数且λk=v.

In this paper, we obtain that the differential polynomial p(w) of a v valued algebroid function w=w(z) is still an algebroid function. In fact, we prove that p(w) can be determined by the equation[ε λ(z)p λ+ε λ-1 (z)p λ-1 +…+ε 0(z)] k=0where ε 0(z),ε 1(z),…ε λ(z) are entire functions of z sharing no common zeros, λ and k are positive integer numbers and satisfy λk=v.