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Multiplicatively badly approximable numbers and generalised Cantor sets

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JournalAdvances in Mathematics
DateE-pub ahead of print - 12 Aug 2011
DatePublished (current) - 1 Dec 2011
Issue number5
Volume228
Number of pages31
Pages (from-to)2766-2796
Early online date12/08/11
Original languageEnglish

Abstract

Let p be a prime number. The p-adic case of the Mixed Littlewood Conjecture states that View the MathML source for all a¿R. We show that with the additional factor of View the MathML source the statement is false. Indeed, our main result implies that the set of a for which View the MathML source is of full dimension. The result is obtained as an application of a general framework for Cantor sets developed in this paper.

    Research areas

  • Diophantine approximation; , Littlewood Conjecture

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