The work of Einsiedler, Katok and Lindenstrauss on the  Littlewood conjecture

Venkatesh, Akshay

doi:10.1090/s0273-0979-07-01194-9

Cited by 20 publications

(21 citation statements)

References 25 publications

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“…This together with (18) and (19), gives via Lemma 1 that | lim sup q→∞ B q | > 0 and thereby proves the divergence case of Theorem 2. The convergence case is a consequence of, for example, Theorem 13 from [17, §5].…”

Section: Proof Of Theoremsupporting

confidence: 66%

Multiplicative zero-one laws and metric number theory

2013

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We develop the classical theory of Diophantine approximation without assuming monotonicity or convexity. A complete 'multiplicative' zero-one law is established akin to the 'simultaneous' zero-one laws of Cassels and Gallagher. As a consequence we are able to establish the analogue of the Duffin-Schaeffer theorem within the multiplicative setup. The key ingredient is the rather simple but nevertheless versatile 'cross fibering principle'. In a nutshell it enables us to 'lift' zero-one laws to higher dimensions.

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Section: Proof Of Theoremsupporting

confidence: 66%

Multiplicative zero-one laws and metric number theory

2013

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“…Einsiedler, Katok, and Lindenstrauss [16] (see also [35]) established that the set of exceptions to the Littlewood conjecture is very small. has Hausdorff dimension zero.…”

Section: The Littlewood Conjecturementioning

confidence: 99%

Around the Littlewood conjecture in Diophantine approximation

Bugeaud¹

2015

Publications Mathématiques De Besançon. Algèbre Et Théorie Des Nombres

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“…The philosophy behind this line of work is that, even if one wants primarily to understand orbit closures, it is more convenient to first work with invariant measures. For a short introduction to this philosophy, see Venkatesh's survey [Ven08].…”

Section: 2mentioning

confidence: 99%