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APPROXIMATING NUMBERS OF THE CANTOR SET BY ALGEBRAIC NUMBERS

Part of: Classical measure theory Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  03 October 2022

YUAN ZHANG Open the ORCID record for YUAN ZHANG [Opens in a new window] ,
JIA LIU Open the ORCID record for JIA LIU [Opens in a new window]  and
SAISAI SHI Open the ORCID record for SAISAI SHI [Opens in a new window]
YUAN ZHANG*
Affiliation:
Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, PR China
JIA LIU
Affiliation:
Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, PR China e-mail: [email protected]
SAISAI SHI
Affiliation:
Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, PR China e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

We consider the set of elements in a translation of the middle-third Cantor set which can be well approximated by algebraic numbers of bounded degree. A doubling dimensional result is given, which enables one to conclude an upper bound on the dimension of the set in question for a generic translation.

Keywords

Diophantine approximationCantor setHausdorff dimensionalgebraic number

MSC classification

Primary: 11J83: Metric theory
Secondary: 28A78: Hausdorff and packing measures
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 2 , April 2023 , pp. 196 - 203
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

This work is supported by the Support Plan for Outstanding Young Talents in Colleges in Anhui Province (Key project) (No. gxyqZD2020021) and the Natural Science Research Project of Anhui University of Finance and Economics (Nos. ACKYC22083, ACKYC22084).

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