Abstract:

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 $f(z)$ .

Key words: entire function, finite order, difference polynomial, uniqueness, zero