On the Littlewood conjecture in simultaneous Diophantine approximation
Number Theory
2012-05-07 v1
Abstract
For any given real number with bounded partial quotients, we construct explicitly continuum many real numbers with bounded partial quotients for which the pair satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions.
Cite
@article{arxiv.math/0511678,
title = {On the Littlewood conjecture in simultaneous Diophantine approximation},
author = {Boris Adamczewski and Yann Bugeaud},
journal= {arXiv preprint arXiv:math/0511678},
year = {2012}
}