A note on expansion in prime fields

Tuomas Orponen, Laura Venieri

Let $\beta ,\epsilon \in (0,1]$, and $k\ge \exp (122\max \{1/\beta ,1/\epsilon \})$. We prove that if $A,B$ are subsets of a prime field ${\mathbb{Z}}_p$, and $|B|\ge p^{\beta }$, then there exists a sum of the…