The Hausdorff Dimension of Sets Arising from Diophantine Approximation with a General Error Function

Research output: Contribution to journalArticle

Abstract

Letm,nbe positive integers and let?:Zn?R be a non-negative function. LetW(m, n; ?) be the setX?Rmn:?j=1nxijqj<?(q), 1=i=m, for infinitely manyq?Zn.The Hausdorff dimension ofW(m, n; ?) is obtained for arbitrary non-negative functions?, with no monotonicity assumptions. © 1998 Academic Press.

Original languageEnglish
Pages (from-to)166-171
Number of pages6
JournalJournal of Number Theory
Volume71
Issue number2
DOIs
Publication statusPublished - Aug 1998

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Diophantine Approximation
Error function
Hausdorff Dimension
Non-negative
Monotonicity
Integer
Arbitrary

Cite this

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abstract = "Letm,nbe positive integers and let?:Zn?R be a non-negative function. LetW(m, n; ?) be the setX?Rmn:?j=1nxijqj<?(q), 1=i=m, for infinitely manyq?Zn.The Hausdorff dimension ofW(m, n; ?) is obtained for arbitrary non-negative functions?, with no monotonicity assumptions. {\circledC} 1998 Academic Press.",
author = "Rynne, {Bryan P.}",
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}

The Hausdorff Dimension of Sets Arising from Diophantine Approximation with a General Error Function. / Rynne, Bryan P.

In: Journal of Number Theory, Vol. 71, No. 2, 08.1998, p. 166-171.

Research output: Contribution to journalArticle

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