Journal of East China Normal University(Natural Science) ›› 2021, Vol. 2021 ›› Issue (1): 28-35.doi: 10.3969/j.issn.1000-5641.201911044

• Mathematics • Previous Articles     Next Articles

Zeros and uniqueness of a class of difference polynomials

Yiping WANG(), Zhigang HUANG*()   

  1. School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou Jiangsu 215000, China
  • Received:2019-11-07 Online:2021-01-25 Published:2021-01-28
  • Contact: Zhigang HUANG;


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

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