On arithmetic properties of Cantor sets

doi:10.1007/s11425-021-1924-1

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	On arithmetic properties of Cantor sets
	Cui, Lu 1,2; Ma, Minghui 1,2
	2022-06-10
发表期刊	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
页码	26
摘要	In this paper, we study three types of Cantor sets. For any integer m >= 4, we show that every real number in [0, k] is the sum of at most k m-th powers of elements in the Cantor ternary set C for some positive integer k, and the smallest such k is 2(m). Moreover, we generalize this result to the middle-1/alpha Cantor set for 1 < alpha < 2 + root 5 and m sufficiently large. For the naturally embedded image W of the Cantor dust C x C into the complex plane C, we prove that for any integer m >= 3, every element in the closed unit disk in C can be written as the sum of at most 2(m+8) m-th powers of elements in W. At last, some similar results on p-adic Cantor sets are also obtained.
关键词	Cantor ternary set Cantor dust p-adic Cantor set Waring's problem
DOI	10.1007/s11425-021-1924-1
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:000812036100002
出版者	SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/61557
专题	中国科学院数学与系统科学研究院
通讯作者	Ma, Minghui
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Cui, Lu,Ma, Minghui. On arithmetic properties of Cantor sets[J]. SCIENCE CHINA-MATHEMATICS,2022:26.
APA	Cui, Lu,&Ma, Minghui.(2022).On arithmetic properties of Cantor sets.SCIENCE CHINA-MATHEMATICS,26.
MLA	Cui, Lu,et al."On arithmetic properties of Cantor sets".SCIENCE CHINA-MATHEMATICS (2022):26.