A polynomial Roth theorem for corners in ${\mathbb{R}}^2$ and a related bilinear singular integral operator

Xuezhi Chen, Jingwei Guo

We prove a quantitative Roth-type theorem for polynomial corners in ${\mathbb{R}}^2$. Let $P_1$ and $P_2$ be two linearly independent polynomials with zero constant term. We show tha…