Research output: Contribution to journal › Article

**Multiplicatively badly approximable numbers and generalised Cantor sets.** / Velani, Sanju; Badziahin, Dzmitry.

Research output: Contribution to journal › Article

Velani, S & Badziahin, D 2011, 'Multiplicatively badly approximable numbers and generalised Cantor sets', *Advances in Mathematics*, vol. 228, no. 5, pp. 2766-2796. https://doi.org/10.1016/j.aim.2011.06.041

Velani, S., & Badziahin, D. (2011). Multiplicatively badly approximable numbers and generalised Cantor sets. *Advances in Mathematics*, *228*(5), 2766-2796. https://doi.org/10.1016/j.aim.2011.06.041

Velani S, Badziahin D. Multiplicatively badly approximable numbers and generalised Cantor sets. Advances in Mathematics. 2011 Dec 1;228(5):2766-2796. https://doi.org/10.1016/j.aim.2011.06.041

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title = "Multiplicatively badly approximable numbers and generalised Cantor sets",

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.",

keywords = "Diophantine approximation; , Littlewood Conjecture",

author = "Sanju Velani and Dzmitry Badziahin",

year = "2011",

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N2 - 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.

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