Exponential multiple mixing for commuting automorphisms of a nilmanifold

Timothée Bénard, Péter P. Varjú

Let $l\in {\mathbb{N}}_{\ge 1}$ and $\alpha :{\mathbb{Z}}^l\to \text{Aut}(\mathcal{N})$ be an action of ${\mathbb{Z}}^l$ by automorphisms on a compact nilmanifold $\mathcal{N}$. We a…