Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case

Sean Prendiville

doi:10.19086/da.1282

Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case

Sean Prendiville

Research output: Contribution to journal › Article › peer-review

Abstract

We obtain quantitative bounds in the polynomial Szemerédi theorem of Bergelson and Leibman, provided the polynomials are homogeneous and of the same degree. Such configurations include arithmetic progressions with common difference equal to a perfect kth power.

Original language	English
Number of pages	34
Journal	Discrete Analysis
Volume	2017
Issue number	5
DOIs	https://doi.org/10.19086/da.1282
Publication status	Published - 21 Feb 2017

Keywords

Bergelson–Leibman theorem
polynomial Szemerédi
Gowers norms
density bounds

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10.19086/da.1282Licence: CC BY

https://arxiv.org/abs/1409.8234v4Licence: CC BY

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title = "Quantitative bounds in the polynomial Szemer{\'e}di theorem: the homogeneous case",

abstract = "We obtain quantitative bounds in the polynomial Szemer{\'e}di theorem of Bergelson and Leibman, provided the polynomials are homogeneous and of the same degree. Such configurations include arithmetic progressions with common difference equal to a perfect kth power.",

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AB - We obtain quantitative bounds in the polynomial Szemerédi theorem of Bergelson and Leibman, provided the polynomials are homogeneous and of the same degree. Such configurations include arithmetic progressions with common difference equal to a perfect kth power.

KW - Bergelson–Leibman theorem

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KW - Gowers norms

KW - density bounds

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JO - Discrete Analysis

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Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case

Abstract

Keywords

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