KMS Of Academy of mathematics and systems sciences, CAS
On arithmetic properties of Cantor sets | |
Cui, Lu1,2; Ma, Minghui1,2 | |
2022-06-10 | |
Source Publication | SCIENCE CHINA-MATHEMATICS |
ISSN | 1674-7283 |
Pages | 26 |
Abstract | 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. |
Keyword | Cantor ternary set Cantor dust p-adic Cantor set Waring's problem |
DOI | 10.1007/s11425-021-1924-1 |
Indexed By | SCI |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000812036100002 |
Publisher | SCIENCE PRESS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/61557 |
Collection | 中国科学院数学与系统科学研究院 |
Corresponding Author | Ma, Minghui |
Affiliation | 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 |
Recommended Citation 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. |
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