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A note on the theorem of Jarník-Besicovitch

Dickinson, H. (1997) A note on the theorem of Jarník-Besicovitch. Glasgow Mathematical Journal, 39 (2). pp. 233-236. ISSN 0017-0895

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Abstract

This note draws together and extends two recent results on Diophantine approximation and Hausdorff dimension. The first, by Hinokuma and Shiga [12], considers the oscillating error function |sin q|/qr rather than the strictly decreasing function q~T of Jarnik's theorem. The second is Rynne's extension [17] to systems of linear forms of Borosh and Fraenkel's paper [3] on restricted Diophantine approximation with real numbers. Rynne's result will be extended to a class of general error functions and applied to obtain a more general form of [12] in which the error function is any positive function.

Item Type: Article
Keywords: Jarnik-Besicovitch; Theorem; Diophantine approximation; Hausdorff dimension.
Subjects: Science & Engineering > Mathematics & Statistics
Item ID: 1569
Identification Number: 10.1017/S0017089500032134
Depositing User: Dr. Detta Dickinson
Date Deposited: 06 Oct 2009 11:55
Journal or Publication Title: Glasgow Mathematical Journal
Publisher: Cambridge University Press
Refereed: Yes
URI:

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