Near diagonal additive energy bound for points on algebraic surfaces

Yifan Jing, Shukun Wu

Let $F:{\mathbb{R}}^3\to \mathbb{R}$ be a polynomial that is irreducible over $\mathbb{R}$ with $\text{deg}F\ge 2$. We prove that, for any finite $X\subset Z(F)$ that does not concen…