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

Abstract

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 fractional dimensions. The proof uses Fourier analysis.

References in corpus (4)

• Arithmetic progressions in sets of fractional dimension
• A polynomial Roth theorem on the real line
• A Non-Linear Roth Theorem for Fractals of Sufficiently Large Dimension
• A Non-Linear Roth Theorem for Sets of Positive Density