New Upper Bound for Sums of Dilates

Albert Bush, Yi Zhao

For $\lambda \in \mathbb{Z}$, let $\lambda \cdot A=\{\lambda a:a\in A\}$. Suppose $r,h\in \mathbb{Z}$ are sufficiently large and comparable to each other. We prove that if $|A+A|\le K|A|$ and…