Uniqueness of difference polynomials

Xiaomei Zhang; Xiang Chen; Xiaomei Zhang; Xiang Chen

doi:10.3934/math.2021608

AIMS Mathematics

2021, Volume 6, Issue 10: 10485-10494. doi: 10.3934/math.2021608

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Theory article

Uniqueness of difference polynomials

Xiaomei Zhang ¹,
Xiang Chen ^{2
,
,}

1.
Department of Basic Courses, Guangzhou Maritime University, Guangzhou 510725, China
2.
School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, China

Received: 16 March 2021 Accepted: 12 July 2021 Published: 20 July 2021
MSC : 30D30

Let $ f(z) $ be a transcendental meromorphic function of finite order and $ c\in\Bbb{C} $ be a nonzero constant. For any $ n\in\Bbb{N}^{+} $, suppose that $ P(z, f) $ is a difference polynomial in $ f(z) $ such as $ P(z, f) = a_{n}f(z+nc)+a_{n-1}f(z+(n-1)c)+\cdots+a_{1}f(z+c)+a_{0}f(z) $, where $ a_{k} (k = 0, 1, 2, \cdots, n) $ are not all zero complex numbers. In this paper, the authors investigate the uniqueness problems of $ P(z, f) $.
- difference polynomial,
- Borel exceptional values,
- uniqueness
Citation: Xiaomei Zhang, Xiang Chen. Uniqueness of difference polynomials[J]. AIMS Mathematics, 2021, 6(10): 10485-10494. doi: 10.3934/math.2021608

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Abstract

Let $ f(z) $ be a transcendental meromorphic function of finite order and $ c\in\Bbb{C} $ be a nonzero constant. For any $ n\in\Bbb{N}^{+} $, suppose that $ P(z, f) $ is a difference polynomial in $ f(z) $ such as $ P(z, f) = a_{n}f(z+nc)+a_{n-1}f(z+(n-1)c)+\cdots+a_{1}f(z+c)+a_{0}f(z) $, where $ a_{k} (k = 0, 1, 2, \cdots, n) $ are not all zero complex numbers. In this paper, the authors investigate the uniqueness problems of $ P(z, f) $.

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