整函数差分唯一性
Uniqueness of Difference about Entire Functions

本文探讨整函数的差分唯一性问题，证明了：设f(z)为开平面有穷级整函数，g（z）=m_i（z）f（z+c_i）+…+m_k（z）f（z+c）为f(z)的差分多项式，其中m_i（z）（i=1，2，…，k）为f的整小函数， c_i（i=1，2，…，k）k个判别的有穷复数。又设a(z)？0为f(z)的一个小函数，若f(z)与g(z)分担0，IM分担a(z) ，则f(z)=g(z) 。

In this paper, we investigate the uniqueness of difference operators about entire function, and prove: let f(z) be an entire function of finite order, k be some positive integers, let a(z) be a small function of f(z) , and let？g（z）=m_i（z）f（z+c_i）+…+m_k（z）f（z+c）？be the difference poly-nomial of f(z) , where？m_i（z）（i=1，2，…，k） ？are the small functions of f(z) , and？c_i（i=1，2，…，k） ？are some finite distinct values. If f(z) and g(z) share 0 CM, and share a(z)IM, then f(z)=g(z) .