整函数及其微分多项式的唯一性

Uniqueness of an Entire function and its Differential Polynomial

本文证明如下定理：设ｆ（ｚ）为非常数整函数，Ｐ（ｆ）－ｆ￣（ｎ）（ｚ）＋ａ＿１（ｚ）ｆ￣（ｎ－１）（ｚ）＋…ａ＿ｎ（ｚ）ｆ（ｚ），其中ａ＿１（ｚ）ａ＿２（ｚ），…ａ＿ｎ（ｚ）为ｆ（ｚ）的小整函数，若ｆ（ｚ）与Ｐ＿（ｆ）以两个互为判别的有穷复数ａ，ｂ为ＣＭ－分担值，且ａ＋ｂ≠０或者，则ｆ≡Ｐ（ｆ）

In this paper we prove the following theorem:Suppose that f(t) is a non-contant en- tire function and P(f)=f￣( n)(z) +a_1(z)f￣(n-1)(z)+…+a_(ri)(z)f(z),where a_1(z),a_2(z),…,a_n(z)are small functions of f(z). If f(z) and P(f) share two distinct finite complex values a,b(count-ing multiplicity),and if a+b≠0 or,then