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

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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. © 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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