FULLY INHOMOGENEOUS MULTIPLICATIVE DIOPHANTINE APPROXIMATION OF BADLY APPROXIMABLE NUMBERS

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 13 May 2021Embargo end date: 01 Jan 2021 English Publisher:WileyJournal:Mathematika, volume 67, pages 639-646 (issn: 0025-5793, eissn: 2041-7942,

Copyright policy )Funded by:UKRI | New techniques for old pr..., RCN | Combinatorial Methods in ...

Authors: Chow, Sam; Zafeiropoulos, Agamemnon;

doi: 10.1112/mtk.12095 , 10.48550/arxiv.2103.03605

arXiv: 2103.03605

FULLY INHOMOGENEOUS MULTIPLICATIVE DIOPHANTINE APPROXIMATION OF BADLY APPROXIMABLE NUMBERS

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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 by Haynes, Jensen and Kristensen. Finally, we establish a similar result involving inhomogeneously badly approximable numbers, making progress towards a problem posed by Pollington, Velani, Zafeiropoulos and Zorin.

This generalises the previous version

Related Organizations

University of Warwick
United Kingdom
Norwegian University of Science and Technology
Norway

Keywords

Continued fractions and generalizations, Hausdorff and packing measures, Mathematics - Number Theory, Metric theory, FOS: Mathematics, Number Theory (math.NT), QA, simultaneous inhomogeneous approximation, Littlewood's conjecture

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