2 problems

Let $(G/\Gamma,\mu_{G/\Gamma},R_\alpha)$ be an ergodic nilsystem, and let $k_1,\ldots,k_\ell\in\mathbb Z$ be nonzero and distinct. For functions…

Let $a\colon\mathbb N\to\mathbb Z$ be strictly increasing. The notions of being good for seminorm control and for degree-$(\ell+1)$ seminorm control along $\ell$-term arithmetic pr…