Metrical musings on Littlewood and friends
Number Theory
2012-04-05 v1
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 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.
Keywords
Cite
@article{arxiv.1204.0938,
title = {Metrical musings on Littlewood and friends},
author = {Alan Haynes and Jonas Lindstrøm Jensen and Simon Kristensen},
journal= {arXiv preprint arXiv:1204.0938},
year = {2012}
}