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

Bryan P. Rynne

doi:10.1006/jnth.1998.2253

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

Bryan P. Rynne

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

5 Citations (Scopus)

Abstract

Letm,nbe positive integers and let?:Zⁿ?R be a non-negative function. LetW(m, n; ?) be the setX?R^mn:?j=1nx_ijq_j<?(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 language	English
Pages (from-to)	166-171
Number of pages	6
Journal	Journal of Number Theory
Volume	71
Issue number	2
DOIs	https://doi.org/10.1006/jnth.1998.2253
Publication status	Published - Aug 1998

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10.1006/jnth.1998.2253

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title = "The Hausdorff Dimension of Sets Arising from Diophantine Approximation with a General Error Function",

abstract = "Letm,nbe positive integers and let?:Zn?R be a non-negative function. LetW(m, n; ?) be the setX?Rmn:?j=1nxijqjn.The Hausdorff dimension ofW(m, n; ?) is obtained for arbitrary non-negative functions?, with no monotonicity assumptions. {\textcopyright} 1998 Academic Press.",

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

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U2 - 10.1006/jnth.1998.2253

DO - 10.1006/jnth.1998.2253

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SP - 166

EP - 171

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 2

ER -

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

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