Additive equations in dense variables via truncated restriction estimates

Kevin Henriot

We study translation-invariant additive equations of the form ${\sum }_{i=1}^s{\lambda }_i\mathbf{P}({\mathbf{n}}_i)=0$ in variables ${\mathbf{n}}_i\in {\mathbb{Z}}^d$, where the ${\lambda }_i$ are nonz…