Dickinson, H.
(1997)
A note on the theorem of JarníkBesicovitch.
Glasgow Mathematical Journal, 39 (2).
pp. 233236.
ISSN 00170895
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.
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