Bengoechea, Paloma and Moshchevitin, Nikolay (2017) Badly approximable points in twisted Diophantine approximation and Hausdorff dimension. Acta Arithmetica. ISSN 1730-6264
Abstract
For any j_1,...,j_n>0 with j_1+...+j_n=1 and any x \in R^n, we consider the set of points y \in R^n for which max_{1\leq i\leq n}(||qx_i-y_i||^{1/j_i})>c/q for some positive constant c=c(y) and all q\in N. These sets are the `twisted' inhomogeneous analogue of Bad(j_1,...,j_n) in the theory of simultaneous Diophantine approximation. It has been shown that they have full Hausdorff dimension in the non-weighted setting, i.e provided that j_i=1/n, and in the weighted setting when x is chosen from Bad(j_1,...,j_n). We generalise these results proving the full Hausdorff dimension in the weighted setting without any condition on x.
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Copyright, Publisher and Additional Information: | © Instytut Matematyczny PAN, 2017. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details | ||||
Keywords: | math.NT | ||||
Dates: |
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Institution: | The University of York | ||||
Academic Units: | The University of York > Faculty of Sciences (York) > Mathematics (York) | ||||
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Depositing User: | Pure (York) | ||||
Date Deposited: | 27 Feb 2017 15:00 | ||||
Last Modified: | 06 Dec 2023 11:44 | ||||
Published Version: | https://doi.org/10.4064/aa8234-11-2016 | ||||
Status: | Published online | ||||
Refereed: | Yes | ||||
Identification Number: | https://doi.org/10.4064/aa8234-11-2016 | ||||
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