Invariant measures and the set of exceptions to Littlewood's conjecture
Dynamical Systems
2007-05-23 v1 Number Theory
Abstract
We classify the measures on SL (k,R)/SL (k,Z) which are invariant and ergodic under the action of the group A of positive diagonal matrices with positive entropy. We apply this to prove that the set of exceptions to Littlewood's conjecture has Hausdorff dimension zero.
Keywords
Cite
@article{arxiv.math/0612721,
title = {Invariant measures and the set of exceptions to Littlewood's conjecture},
author = {Manfred Einsiedler and Anatole Katok and Elon Lindenstrauss},
journal= {arXiv preprint arXiv:math/0612721},
year = {2007}
}
Comments
48 pages