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
This note draws together and extends two recent results on Diophantine approximation and Hausdorff dimension. The first, by Hinokuma and Shiga , 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  to systems of linear forms of Borosh and Fraenkel's paper  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  in which the error function is any positive function.
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