Uniqueness of difference polynomials

AIMS Mathematics

Xiaomei Zhang¹  Xiang Chen² 

[1] 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;

关键词: difference polynomial;    borel exceptional values;    uniqueness;   

DOI  :  10.3934/math.2021608

来源: DOAJ

【 摘 要 】

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) $.

【 授权许可】

Unknown