Around Furstenberg's times $p$, times $q$ conjecture: times $p$-invariant measures with some large Fourier coefficients

Catalin Badea, Sophie Grivaux

For each integer $n\ge 1$, denote by $T_n$ the map $x\mapsto nx\mathrm{mod}1$ from the circle group $\mathbb{T}=\mathbb{R}/\mathbb{Z}$ into itself. Let $p,q\ge 2$ be two multiplicativ…