亚纯函数与其差分分担值的唯一性

The Uniqueness of Meromorphic Functions and Their Differences Shared Values

运用亚纯函数值分布理论,研究亚纯函数具有三个分担值的唯一性问题.结果表明:非常数亚纯函数f(z)与g(z)分担0,∞CM(记重数)且f^(n)(z)与g^(n)(z)分担aCM,则或者f(z)=tg(z),其中t^(n)=1;或者f(z)=be^(α(z)),g(z)=ce^(-α(z)),其中α(z)为整函数,b,c为非零常数且b^(n)c^(n)=a^(2).并将其应用到亚纯函数k阶线性差分算子的唯一性问题中.

In this paper,we mainly discussed the uniqueness of meromorphic functions sharing three values by using the knowledge of value distribution theory and the following results were proved:let meromorphic functions f(z)and g(z)sharing 0and∞CM,f^(n)(z)and g^(n)(z)sharing aCM,then either f(z)=tg(z),where t^(n)=1,f(z)=be^(α(z)),g(z)=ce^(-α(z)),whereα(z)be a entire function,b,c be nonzero constant and b^(n)c^(n)=a^(2).It is applied to the uniqueness problem of k-order linear difference operator of meromorphic function.