{"title":"SOME RESULTS ON COMPLEX DIFFERENTIAL-DIFFERENCE ANALOGUE OF BRÜCK CONJECTURE","authors":"Min Chen, Zongsheng Gao","doi":"10.4134/CKMS.C160123","DOIUrl":null,"url":null,"abstract":"Abstract. In this paper, we utilize the Nevanlinna theory and uniqueness theory of meromorphic function to investigate the differential-difference analogue of Brück conjecture. In other words, we consider ∆ηf(z) = f(z+η)−f(z) and f (z) share one value or one small function, and then obtain the precise expression of transcendental entire function f(z) under certain conditions, where η ∈ C \\ {0} is a constant such that f(z + η) − f(z) 6≡ 0.","PeriodicalId":45637,"journal":{"name":"Communications of the Korean Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2017-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications of the Korean Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4134/CKMS.C160123","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract. In this paper, we utilize the Nevanlinna theory and uniqueness theory of meromorphic function to investigate the differential-difference analogue of Brück conjecture. In other words, we consider ∆ηf(z) = f(z+η)−f(z) and f (z) share one value or one small function, and then obtain the precise expression of transcendental entire function f(z) under certain conditions, where η ∈ C \ {0} is a constant such that f(z + η) − f(z) 6≡ 0.
期刊介绍：
This journal endeavors to publish significant research and survey of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of four issues (January, April, July, October).
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
