Metrical musings on Littlewood and friends

A. Haynes, Jonas Lindstrøm Jensen, Simon Kristensen

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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.
Original languageEnglish
PublisherDepartment of Mathematics, Aarhus University
Number of pages10
Publication statusPublished - 2012
SeriesPreprints
Number4
ISSN1397-4076

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