Sum of dilates in vector spaces. (English) Zbl 1397.11017
Summary: Let \(d\geq 2\), \(A\subset \mathbb{Z}^d\) be finite and not contained in a translate of any hyperplane, and \(q\in\mathbb{Z}\) such that \(|q|\geq 2\). We show
\[ |A + q\cdot A|\geq (|q|+d+1)|A|- O(1). \]
\[ |A + q\cdot A|\geq (|q|+d+1)|A|- O(1). \]
MSC:
| 11B13 | Additive bases, including sumsets |
| 11B30 | Arithmetic combinatorics; higher degree uniformity |
| 11P70 | Inverse problems of additive number theory, including sumsets |
