Adamczewski Boris & Yann Bugeaud
On the independence of expansions of algebraic numbers
Let $b \ge 2$ be an integer. According to a conjecture of
\'Emile Borel, the $b$adic expansion of any irrational algebraic
number behaves in some respect `like a random sequence'. We give a
contribution to the following related problem:
let $\alpha$ and $\alpha'$ be irrational algebraic
numbers, prove that their $b$adic expansions
either have the same tail, or behave in some respect
`like independent random sequences'.
