亚纯函数及其微分多项式的唯一性

Unicity for Meromorphic Function and ItsDifferential Polynomial

中文关键词:  亚纯函数  整函数  微分多项式  分担函数

英文关键词:Meromorphic function  entire function  differential polynomial  sharing func-tion.

中文摘要:

      设f是非常数亚纯函数,g是f的线性微分多项式．a和b是f的两个不同的小函数．本文证明如果f和g几乎CM分担a和b,则f≡g;此外,若f是非常数整函数,且f和f^(k)(k≥1)IM分担a和b,b-a≠Pe^λz,测f≡g．

英文摘要:

      In this paper we proved the following theorem: Suppose that f is a nonconstantmeromorphic function, and g is a linear differential polynomial of f. a and b are two distinctsmall functions with respect to f. If f and g share a and b almost CM, then f≡g. Moreoverwe also solved the problem posed by [4]: Suppose that f is a nonconstant entire function, aand b are two distinct small functions of f. If f and f^(k)(k ≥1 ) share a and b IM, and b-a≠Pe^λz then f≡g.