On arithmetic properties of Cantor sets
Cui, Lu1,2; Ma, Minghui1,2
AbstractIn 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.
KeywordCantor ternary set Cantor dust p-adic Cantor set Waring's problem
Indexed BySCI
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000812036100002
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Document Type期刊论文
Corresponding AuthorMa, Minghui
Affiliation1.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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