English

On the Littlewood conjecture in simultaneous Diophantine approximation

Number Theory 2012-05-07 v1

Abstract

For any given real number α\alpha with bounded partial quotients, we construct explicitly continuum many real numbers β\beta with bounded partial quotients for which the pair (α,β)(\alpha, \beta) satisfies a strong form of the Littlewood conjecture. Our proof is elementary and rests on the basic theory of continued fractions.

Keywords

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}
}
R2 v1 2026-07-22T17:27:59.092Z