Multiplicatively badly approximable numbers and generalised Cantor sets

TY - JOUR

T1 - Multiplicatively badly approximable numbers and generalised Cantor sets

AU - Velani, Sanju

AU - Badziahin, Dzmitry

PY - 2011/12/1

Y1 - 2011/12/1

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.

AB - 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.

KW - Diophantine approximation;

KW - Littlewood Conjecture

UR - http://www.scopus.com/inward/record.url?scp=81155159814&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2011.06.041

DO - 10.1016/j.aim.2011.06.041

M3 - Article

SN - 0001-8708

VL - 228

SP - 2766

EP - 2796

JO - Advances in Mathematics

JF - Advances in Mathematics

IS - 5

ER -