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1 April 2019 On the polynomial Szemerédi theorem in finite fields
Sarah Peluse
Duke Math. J. 168(5): 749-774 (1 April 2019). DOI: 10.1215/00127094-2018-0051

Abstract

Let P1,,PmZ[y] be any linearly independent polynomials with zero constant term. We show that there exists γ>0 such that any subset of Fq of size at least q1γ contains a nontrivial polynomial progression x,x+P1(y),,x+Pm(y), provided that the characteristic of Fq is large enough.

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Sarah Peluse. "On the polynomial Szemerédi theorem in finite fields." Duke Math. J. 168 (5) 749 - 774, 1 April 2019. https://doi.org/10.1215/00127094-2018-0051

Information

Received: 8 February 2018; Revised: 11 October 2018; Published: 1 April 2019
First available in Project Euclid: 1 February 2019

zbMATH: 07055192
MathSciNet: MR3934588
Digital Object Identifier: 10.1215/00127094-2018-0051

Subjects:
Primary: 11B30
Secondary: 11B25

Keywords: finite fields , Szemerédi’s theorem

Rights: Copyright © 2019 Duke University Press

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Vol.168 • No. 5 • 1 April 2019
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