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Approximating numbers of the cantor set by algebraic numbers

YUAN ZHANG,JIA LIU,SAISAI SHI

Bulletin of the Australian Mathematical Society（2022）

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Abstract
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.
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Key words
Diophantine approximation,Cantor set,Hausdorff dimension,algebraic number
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