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Fully inhomogeneous multiplicative diophantine approximation of badly approximable numbers
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Chow, Sam and Zafeiropoulos, Agamemnon (2021) Fully inhomogeneous multiplicative diophantine approximation of badly approximable numbers. Mathematika, 67 (3). pp. 639-646. doi:10.1112/mtk.12095 ISSN 0025-5793.
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Official URL: http://dx.doi.org/10.1112/mtk.12095
Abstract
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensional set of pairs of badly approximable numbers on a vertical line. We also prove a uniform assertion of this nature, generalising a strong form of a result of Haynes et al. Finally, we establish a similar result involving inhomogeneously badly approximable numbers, making progress towards a problem posed by Pollington et al.
Item Type: | Journal Article | ||||||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||||||
Library of Congress Subject Headings (LCSH): | Diophantine approximation, Number theory | ||||||||||||
Journal or Publication Title: | Mathematika | ||||||||||||
Publisher: | London Mathematical Society | ||||||||||||
ISSN: | 0025-5793 | ||||||||||||
Official Date: | July 2021 | ||||||||||||
Dates: |
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Volume: | 67 | ||||||||||||
Number: | 3 | ||||||||||||
Page Range: | pp. 639-646 | ||||||||||||
DOI: | 10.1112/mtk.12095 | ||||||||||||
Status: | Peer Reviewed | ||||||||||||
Publication Status: | Published | ||||||||||||
Reuse Statement (publisher, data, author rights): | This is the peer reviewed version of the following article: Chow, S. and Zafeiropoulos, A. (2021), Fully inhomogeneous multiplicative diophantine approximation of badly approximable numbers. Mathematika, 67: 639-646. https://doi.org/10.1112/mtk.12095, which has been published in final form at http://dx.doi.org/10.1112/mtk.12095. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. | ||||||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
Date of first compliant deposit: | 27 May 2021 | ||||||||||||
Date of first compliant Open Access: | 28 May 2021 | ||||||||||||
RIOXX Funder/Project Grant: |
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