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Metrical musings on Littlewood and friends


Authors: A. Haynes, J. L. Jensen and S. Kristensen
Journal: Proc. Amer. Math. Soc. 142 (2014), 457-466
MSC (2010): Primary 11J83, 11H46
DOI: https://doi.org/10.1090/S0002-9939-2013-11921-0
Published electronically: November 19, 2013
MathSciNet review: 3133988
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove a metrical result on a family of conjectures related to the Littlewood conjecture, namely the original Littlewood conjecture, the mixed Littlewood conjecture of de Mathan and Teulié, and a hybrid between a conjecture of Cassels and the Littlewood conjecture. It is shown that the set of numbers satisfying a strong version of all of these conjectures is large in the sense of Hausdorff dimension restricted to the set of badly approximable numbers.


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Additional Information

A. Haynes
Affiliation: Department of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, United Kingdom
Address at time of publication: Department of Mathematics, University of York, Heslington, York, YO10 5DD, United Kingdom
Email: akh502@york.ac.uk

J. L. Jensen
Affiliation: Department of Mathematics, Aarhus University, Ny Munkegade 118, DK-8000 Aarhus C, Denmark
Email: jonas@imf.au.dk

S. Kristensen
Affiliation: Department of Mathematics, Aarhus University, Ny Munkegade 118, DK-8000 Aarhus C, Denmark
Email: sik@imf.au.dk

DOI: https://doi.org/10.1090/S0002-9939-2013-11921-0
Received by editor(s): April 4, 2012
Published electronically: November 19, 2013
Additional Notes: The first author was supported by EPSRC grant EP/J00149X/1
The third author’s research was supported by the Danish Research Council for Independent Research
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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