On the complexity of a putative counterexample to the $p$-adic Littlewood conjecture

Dmitry Badziahin, Yann Bugeaud, Manfred Einsiedler +1

Let $||\cdot ||$ denote the distance to the nearest integer and, for a prime number $p$, let $|\cdot {|}_p$ denote the $p$-adic absolute value. In 2004, de Mathan and Teulié asked…