Quantitative bounds in the non-linear Roth theorem

Peluse, Sarah and Prendiville, Sean (2019) Quantitative bounds in the non-linear Roth theorem. arXiv.

Full text not available from this repository.

Abstract

We show that any subset of $[N]$ of density at least $(\log\log{N})^{-2^{-157}}$ contains a nontrivial progression of the form $x,x+y,x+y^2$. This is the first quantitatively effective version of the Bergelson--Leibman polynomial Szemer\'edi theorem for a progression involving polynomials of differing degrees. In the course of the proof, we also develop a quantitative version of a special case of a concatenation theorem of Tao and Ziegler, with polynomial bounds.

Item Type:
Journal Article
Journal or Publication Title:
arXiv
ID Code:
138922
Deposited By:
Deposited On:
13 Nov 2019 11:40
Refereed?:
Yes
Published?:
Published
Last Modified:
08 Oct 2020 08:38