Generalized polynomials and hyperplane functions in $(\mathbb{Z}/p^k\mathbb{Z}{)}^n$

Izabella Łaba, Charlotte Trainor

For $p$ prime, let ${\mathcal{H}}^n$ be the linear span of characteristic functions of hyperplanes in $(\mathbb{Z}/p^k\mathbb{Z}{)}^n$. We establish new upper bounds on the dimension o…