Sum of dilates in vector spaces

Abstract

Let $d\ge 2$, $A\subset {\mathbb{Z}}^d$ be finite and not contained in a translate of any hyperplane, and $q\in \mathbb{Z}$ such that $|q|>1$. We show $$|A+q\cdot A|\ge (|q|+d+1)|A|-O_{q,d}(1).$$

References in corpus (1)

• A Lower Bound for the Size of a Sum of Dilates