3 problems

Let $K$ be a global field with ring of integers $\mathcal{O}_K$. Let $P_1[x],\dots,P_k[x]\in\mathcal{O}_K[x]$ be nonconstant polynomials, and let $d^*(A)$ denote the upper Banach d…

For fixed integers $m$ and $k\geq 2$, let $R\subseteq\{0,1,\dots,m-1\}$ be a set whose differences between distinct elements never equal a $k$th power modulo $m$. Write … Ruzsa's c…

Let $p_1,\ldots,p_r:\mathbb Z^m\to\mathbb Z^k$ be polynomial mappings. For a set $E\subseteq\mathbb Z^k$ of positive upper Banach density, define … The family has the SPSZ property…