Zeros and uniqueness of a class of difference polynomials

WANG Yiping; HUANG Zhigang

doi:10.3969/j.issn.1000-5641.201911044

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WANG Yiping, HUANG Zhigang. Zeros and uniqueness of a class of difference polynomials[J]. Journal of East China Normal University (Natural Sciences), 2021, (1): 28-35. doi: 10.3969/j.issn.1000-5641.201911044

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WANG Yiping, HUANG Zhigang. Zeros and uniqueness of a class of difference polynomials[J]. Journal of East China Normal University (Natural Sciences), 2021, (1): 28-35. doi: 10.3969/j.issn.1000-5641.201911044

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Zeros and uniqueness of a class of difference polynomials

doi: 10.3969/j.issn.1000-5641.201911044

WANG Yiping,
HUANG Zhigang^,

School of Mathematics and Physics, Suzhou University of Science and Technology, Suzhou Jiangsu　215000, China

Received Date: 2019-11-07
Publish Date: 2021-01-27

Abstract

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 $f(z)$.
- entire function,
- finite order,
- difference polynomial,
- uniqueness,
- zero

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References(19)

References

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