Home > Research > Publications & Outputs > Quantitative bounds in the non-linear Roth theorem

Research

Associated organisational units

Links

View graph of relations

Quantitative bounds in the non-linear Roth theorem

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

Standard

Quantitative bounds in the non-linear Roth theorem. / Peluse, Sarah; Prendiville, Sean.
In: arXiv, 06.03.2019.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Peluse, S & Prendiville, S 2019, 'Quantitative bounds in the non-linear Roth theorem', arXiv. <https://arxiv.org/abs/1903.02592>

APA

Peluse, S., & Prendiville, S. (2019). Quantitative bounds in the non-linear Roth theorem. arXiv. https://arxiv.org/abs/1903.02592

Vancouver

Peluse S, Prendiville S. Quantitative bounds in the non-linear Roth theorem. arXiv. 2019 Mar 6.

Author

Peluse, Sarah ; Prendiville, Sean. / Quantitative bounds in the non-linear Roth theorem. In: arXiv. 2019.

Bibtex

@article{2fdcf65d3f8748718f72dd86321fd2b0,
title = "Quantitative bounds in the non-linear Roth theorem",
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.",
author = "Sarah Peluse and Sean Prendiville",
year = "2019",
month = mar,
day = "6",
language = "English",
journal = "arXiv",

}

RIS

TY - JOUR

T1 - Quantitative bounds in the non-linear Roth theorem

AU - Peluse, Sarah

AU - Prendiville, Sean

PY - 2019/3/6

Y1 - 2019/3/6

N2 - 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.

AB - 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.

M3 - Journal article

JO - arXiv

JF - arXiv

ER -