Two bipolynomial Roth theorems in $\mathbb{R}$

Xuezhi Chen, Jingwei Guo, Xiaochun Li

We give two Roth theorems, related to the nonlinear configuration $x$, $x+P_1(t)$, $x+P_2(t)$ involving two polynomials, for sets in $\mathbb{R}$ of positive density and of fractio…