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

Manfred Einsiedler; Anatole Katok; Elon Lindenstrauss

doi:10.4007/annals.2006.164.513

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

Manfred Einsiedler^*, Anatole Katok, Elon Lindenstrauss

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

113 Scopus citations

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.

Original language	English
Pages (from-to)	513-560
Number of pages	48
Journal	Annals of Mathematics
Volume	164
Issue number	2
DOIs	https://doi.org/10.4007/annals.2006.164.513
State	Published - Sep 2006
Externally published	Yes

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title = "Invariant measures and the set of exceptions to Littlewood's conjecture",

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.",

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AB - 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.

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

Abstract

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