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Quantitative bounds in the non-linear Roth theorem

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

In: arXiv, 06.03.2019.

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@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 -