Uniqueness of difference polynomials
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_...
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| Format: | Article |
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AIMS Press
2021-07-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021608?viewType=HTML |
| _version_ | 1818888243277463552 |
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| author | Xiaomei Zhang Xiang Chen |
| author_facet | Xiaomei Zhang Xiang Chen |
| author_sort | Xiaomei Zhang |
| collection | DOAJ |
| description | 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) $. |
| first_indexed | 2024-12-19T16:50:02Z |
| format | Article |
| id | doaj.art-be3559b961664e76ac41e9c8797e48d6 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-19T16:50:02Z |
| publishDate | 2021-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-be3559b961664e76ac41e9c8797e48d62022-12-21T20:13:34ZengAIMS PressAIMS Mathematics2473-69882021-07-01610104851049410.3934/math.2021608Uniqueness of difference polynomialsXiaomei Zhang 0Xiang Chen11. Department of Basic Courses, Guangzhou Maritime University, Guangzhou 510725, China2. School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, ChinaLet $ 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) $.https://www.aimspress.com/article/doi/10.3934/math.2021608?viewType=HTMLdifference polynomialborel exceptional valuesuniqueness |
| spellingShingle | Xiaomei Zhang Xiang Chen Uniqueness of difference polynomials AIMS Mathematics difference polynomial borel exceptional values uniqueness |
| title | Uniqueness of difference polynomials |
| title_full | Uniqueness of difference polynomials |
| title_fullStr | Uniqueness of difference polynomials |
| title_full_unstemmed | Uniqueness of difference polynomials |
| title_short | Uniqueness of difference polynomials |
| title_sort | uniqueness of difference polynomials |
| topic | difference polynomial borel exceptional values uniqueness |
| url | https://www.aimspress.com/article/doi/10.3934/math.2021608?viewType=HTML |
| work_keys_str_mv | AT xiaomeizhang uniquenessofdifferencepolynomials AT xiangchen uniquenessofdifferencepolynomials |