Rational points in translations of the Cantor set

Kan Jiang; Derong Kong; Wenxia Li; Zhiqiang Wang

doi:10.1016/j.indag.2024.03.012

Rational points in translations of the Cantor set

Kan Jiang
, Derong Kong
, Wenxia Li
, Zhiqiang Wang^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Given two coprime integers p≥2 and q≥3, let D_p⊂[0,1) consist of all rational numbers which have a finite p-ary expansion, and let [Formula presented] where A⊂0,1,…,q−1 with cardinality 1<#A<q. In 2021 Schleischitz showed that #(D_p∩K(q,A))<+∞. In this paper we show that for any r∈Q and for any α∈R, #((rD_p+α)∩K(q,A))<+∞.

Original language	English
Pages (from-to)	516-522
Number of pages	7
Journal	Indagationes Mathematicae
Volume	35
Issue number	3
DOIs	https://doi.org/10.1016/j.indag.2024.03.012
State	Published - May 2024

Keywords

Cantor set
Rational number
q-ary expansion

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10.1016/j.indag.2024.03.012

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title = "Rational points in translations of the Cantor set",

abstract = "Given two coprime integers p≥2 and q≥3, let Dp⊂[0,1) consist of all rational numbers which have a finite p-ary expansion, and let [Formula presented] where A⊂0,1,…,q−1 with cardinality 1<\#Ap∩K(q,A))<+∞. In this paper we show that for any r∈Q and for any α∈R, \#((rDp+α)∩K(q,A))<+∞.",

keywords = "Cantor set, Rational number, q-ary expansion",

author = "Kan Jiang and Derong Kong and Wenxia Li and Zhiqiang Wang",

note = "Publisher Copyright: {\textcopyright} 2024 Royal Dutch Mathematical Society (KWG)",

year = "2024",

month = may,

doi = "10.1016/j.indag.2024.03.012",

language = "英语",

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T1 - Rational points in translations of the Cantor set

AU - Jiang, Kan

AU - Kong, Derong

AU - Li, Wenxia

AU - Wang, Zhiqiang

PY - 2024/5

Y1 - 2024/5

N2 - Given two coprime integers p≥2 and q≥3, let Dp⊂[0,1) consist of all rational numbers which have a finite p-ary expansion, and let [Formula presented] where A⊂0,1,…,q−1 with cardinality 1<#Ap∩K(q,A))<+∞. In this paper we show that for any r∈Q and for any α∈R, #((rDp+α)∩K(q,A))<+∞.

AB - Given two coprime integers p≥2 and q≥3, let Dp⊂[0,1) consist of all rational numbers which have a finite p-ary expansion, and let [Formula presented] where A⊂0,1,…,q−1 with cardinality 1<#Ap∩K(q,A))<+∞. In this paper we show that for any r∈Q and for any α∈R, #((rDp+α)∩K(q,A))<+∞.

KW - Cantor set

KW - Rational number

KW - q-ary expansion

UR - https://www.scopus.com/pages/publications/85190810042

U2 - 10.1016/j.indag.2024.03.012

DO - 10.1016/j.indag.2024.03.012

M3 - 文章

AN - SCOPUS:85190810042

SN - 0019-3577

VL - 35

SP - 516

EP - 522

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 3

ER -

Rational points in translations of the Cantor set

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Keywords

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