Polynomial actions of unitary operators and idempotent ultrafilters

Vitaly Bergelson, Stanisław Kasjan, Mariusz Lemańczyk

Let $p$ be an idempotent ultrafilter over $\mathbb{N}$. For a positive integer $N$, let ${\mathcal{P}}_{\le N}$ denote the additive group of polynomials $P\in \mathbb{Z}[x]$ with ${\rm…