Higher order difference operators and uniqueness of meromorphic functions

doi:10.1007/s13324-021-00529-w

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	Higher order difference operators and uniqueness of meromorphic functions
	Fang, Mingliang 1; Wang, Yuefei 2,3
	2021-06-01
发表期刊	ANALYSIS AND MATHEMATICAL PHYSICS
ISSN	1664-2368
卷号	11 期号:2 页码:13
摘要	It is a known uniqueness result that if f is a transcendental meromorphic function of finite order with two Borel excetional values a not equal infinity, b and its first order difference operator Delta(c)f not equivalent to 0, for some complex number c, and if f and Delta(c)f share a, b CM, then a = 0, b = infinity and f = exp(Az + B), where A not equal 0, B is an element of C. This type of results has its origin dating back to Csillag-Tumura's uniqueness theorems. In this paper, by using completely different methods, we shall show that the result holds for arbitrary higher order difference operators. Examples are provided to show that this result is not valid for meromorphic functions with infinite order, which also shows a distinction between the derivatives and the difference operators of meromorphic functions, in view of Csillag-Tumura type uniqueness theorems.
关键词	Meromorphic functions Value distribution Borel exceptional values Differences
DOI	10.1007/s13324-021-00529-w
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000638127300001
出版者	SPRINGER BASEL AG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58415
专题	中国科学院数学与系统科学研究院
通讯作者	Fang, Mingliang
作者单位	1.Hangzhou Dianzi Univ, Dept Math, Hangzhou 310018, Peoples R China 2.Shenzhen Univ, Sch Math & Stat, Shenzhen 518060, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Fang, Mingliang,Wang, Yuefei. Higher order difference operators and uniqueness of meromorphic functions[J]. ANALYSIS AND MATHEMATICAL PHYSICS,2021,11(2):13.
APA	Fang, Mingliang,&Wang, Yuefei.(2021).Higher order difference operators and uniqueness of meromorphic functions.ANALYSIS AND MATHEMATICAL PHYSICS,11(2),13.
MLA	Fang, Mingliang,et al."Higher order difference operators and uniqueness of meromorphic functions".ANALYSIS AND MATHEMATICAL PHYSICS 11.2(2021):13.