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.
- Publication:
-
arXiv e-prints
- Pub Date:
- August 2020
- DOI:
- 10.48550/arXiv.2008.13011
- arXiv:
- arXiv:2008.13011
- Bibcode:
- 2020arXiv200813011C
- Keywords:
-
- Mathematics - Classical Analysis and ODEs