Sum of Many Dilates

Abstract

We show that for any coprime integers $\lambda_1 , \ldots , \lambda_k$ and any finite $A \subset \mathbb{Z}$, one has $$|\lambda_1 \cdot A + \ldots + \lambda_k \cdot A| \geq (|\lambda_1| + \ldots + |\lambda_k|)|A|- C,$$ where $C$ only depends on $\lambda_1 , \ldots , \lambda_k$.

Locations

• arXiv (Cornell University) - View - PDF
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• Combinatorics Probability Computing - View