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Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
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Date | Accepted/In press - 23 Jan 2017 |

Date | E-pub ahead of print - 5 Apr 2017 |

Date | Published (current) - May 2018 |

Issue number | 3 |

Volume | 164 |

Number of pages | 47 |

Pages (from-to) | 413-459 |

Early online date | 5/04/17 |

Original language | English |

We solve the problem of giving sharp asymptotic bounds on the Hausdorff dimensions of certain sets of badly approximable matrices, thus improving results of Broderick and Kleinbock (preprint 2013) as well as Weil (preprint 2013), and generalizing to higher dimensions those of Kurzweil ('51) and Hensley ('92). In addition we use our technique to compute the Hausdorff $f$-measure of the set of matrices which are not $\psi$-approximable, given a dimension function $f$ and a function $\psi:(0,\infty)\to (0,\infty)$. This complements earlier work by Dickinson and Velani ('97) who found the Hausdorff $f$-measure of the set of matrices which are $\psi$-approximable.

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- math.NT

## Programme Grant-New Frameworks in metric Number Theory

Project: Research project (funded) › Research

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