Near optimal three-fold additive energy bound for points on convex curves

Adam Cushman, Ciprian Demeter, Shukun Wu

Let $X\subset \mathbb{R}$ be finite and let $\gamma (t)=(t,f(t))$, where $f$ is strictly convex. We show that \[ J_3(γ(X)) =\#\{(x_1,\ldots,x_6)\in X^6:\sum_{i=1}^3γ(x_i)=\sum_{i=4}^6γ(x_…