Invariant measures and the set of exceptions to Littlewood's conjecture

2006/12/22 by Manfred Einsiedler, Anatole Katok, Elon Lindenstrauss · 2 citations
Mathematics · #math.DS #math.NT

paper · pdf

published as Ann. of Math. (2) 164 (2006), no. 2, 513--560 · 48 pages

arxiv created 2006/12/22 · arxiv updated 2009/12/01

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.

Cited by

• Bounded diagonal orbits in homogeneous spaces over function fields
• Hausdorff measure and Fourier dimensions of limsup sets arising in weighted and multiplicative Diophantine approximation