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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. |
| Academic Unit: | Faculty of Science and Engineering > Mathematics and 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 |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/1569 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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