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- W4298217596 abstract "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." @default.
- W4298217596 created "2022-10-01" @default.
- W4298217596 creator A5045774747 @default.
- W4298217596 date "2015-09-13" @default.
- W4298217596 modified "2023-09-23" @default.
- W4298217596 title "A Hausdorff measure version of the Jarn'ik--Schmidt theorem in Diophantine approximation" @default.
- W4298217596 doi "https://doi.org/10.48550/arxiv.1509.03885" @default.
- W4298217596 hasPublicationYear "2015" @default.
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