Sum of many dilates

Abstract

We show that for any coprime integers ${\lambda }_1,\dots ,{\lambda }_k$ and any finite $A\subset \mathbb{Z}$, one has $$|{\lambda }_1\cdot A+\dots +{\lambda }_k\cdot A|\ge (|{\lambda }_1|+\dots +|{\lambda }_k|)|A|-C,$$ where $C$ only depends on ${\lambda }_1,\dots ,{\lambda }_k$.

Minor changes, computed constant explicitly

References in corpus (2)

• Sums of dilates in groups of prime order
• A Lower Bound for the Size of a Sum of Dilates

Cited by in corpus (2)

• Sums of dilates in ordered groups
• A question of Bukh on sums of dilates