{"title":"Zero distribution of some difference polynomials","authors":"Qian Li, Dan Liu, Zhi-bo Huang","doi":"10.1007/s11766-023-4179-9","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, suppose that <i>a, c</i> ∈ ℂ {0}, <i>c</i><sub><i>j</i></sub> ∈ ℂ(<i>j</i> = 1, 2, ⋯, <i>n</i>) are not all zeros and <i>n</i> ≥ 2, and <i>f</i>(<i>z</i>) is a finite order transcendental entire function with Borel finite exceptional value or with infinitely many multiple zeros, the zero distribution of difference polynomials of <i>f</i>(<i>z</i> + <i>c</i>) − <i>af</i><sup>n</sup>(<i>z</i>) and <i>f</i>(<i>z</i>)<i>f</i>(<i>z</i> + <i>c</i><sub>1</sub>) ⋯ <i>f</i>(<i>z</i> + <i>c</i><sub><i>n</i></sub>) are investigated. A number of examples are also presented to show that our results are best possible in a certain sense.</p></div>","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":"38 3","pages":"392 - 402"},"PeriodicalIF":1.0000,"publicationDate":"2023-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics-A Journal of Chinese Universities Series B","FirstCategoryId":"1089","ListUrlMain":"https://link.springer.com/article/10.1007/s11766-023-4179-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, suppose that a, c ∈ ℂ {0}, cj ∈ ℂ(j = 1, 2, ⋯, n) are not all zeros and n ≥ 2, and f(z) is a finite order transcendental entire function with Borel finite exceptional value or with infinitely many multiple zeros, the zero distribution of difference polynomials of f(z + c) − afn(z) and f(z)f(z + c1) ⋯ f(z + cn) are investigated. A number of examples are also presented to show that our results are best possible in a certain sense.
期刊介绍：
Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects.
The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry.
Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.
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