主要运用Nevanlinna值分布理论研究了差分多项式的唯一性和零点分布, 得到了关于差分多项式 $P(f)\sum_{i=1}^{k}t_{i}f(z+c_{i})$ 的唯一性结果和关于差分多项式 $P(f)\big(\sum_{i=1}^{k}b_{i}(z)f(z+c_{i})\big)^s-b_0(z)$ 的零点分布结果, 其中 $f(z)$ 是有限级超越整函数, $c_{i}, t_{i}\;(i=1,2, \cdots, k)$ 是非零复常数, $b_{i}(z)\;(i=0, 1, \cdots, k)$ 是关于 $f(z)$ 的小函数.

In this paper, we investigate the uniqueness and distribution of zeros of a class of difference polynomials by using Nevanlinna’s value distribution theory. We obtain results about the uniqueness of the difference polynomials $P(f)\sum_{i=1}^{k}t_{i}f(z+c_{i})$ and the distribution of zeros of the difference polynomials $P(f)(\sum_{i=1}^{k}b_{i}(z)f(z+c_{i}))^s-b_0(z)$ , where $f(z)$ is a transcendental entire function of finite order, $c_i, t_i\;(i=1, 2, \cdots,k)$ are non-zero constants, and $b_i(z)\;(i=0, 1, \cdots,k)$ are small functions with respect to $f(z)$ .