English

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