Metrical musings on Littlewood and friends

Details Metrical musings on Littlewood and friends Metrical musings on Littlewood and friends

2012-04-04

arxiv.org/abs/1204.0938v1

Mathematics

Number Theory

Scientific paper

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 Teuli\'e 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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