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Metrical musings on Littlewood and friends

By A. Haynes, J. L. Jensen and S. Kristensen
No. 04, April 2012

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.

2000 Mathematics Subject Classification. 11J83, 11H46.

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