Open AccessUniqueness of difference polynomials
Author(s) -
Xiaomei Zhang,
Xiang Chen
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
ISSN - 2473-6988
DOI - 10.3934/math.2021608
Subject(s) - meromorphic function , uniqueness , transcendental number , mathematics , combinatorics , zero (linguistics) , polynomial , entire function , order (exchange) , function (biology) , constant (computer programming) , pure mathematics , mathematical analysis , philosophy , linguistics , finance , evolutionary biology , computer science , economics , biology , programming language
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) $.