Adamczewski Boris & Yann Bugeaud
On the Littlewood conjecture in simultaneous Diophantine approximation
For any given $\alpha$ with bounded partial quotients, we give an explicit
construction of continuum many independent real numbers $\beta$ with bounded
partial quotients for which the pair $(\alpha,\beta)$ satisfies a strong
form of the Littlewood conjecture. Our proof is elementary and rests on
the basic theory of continued fractions.
