On the polynomial szemerédi theorem in finite fields

Sarah Peluse

doi:10.1215/00127094-2018-0051

On the polynomial szemerédi theorem in finite fields

Sarah Peluse

Mathematics

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

17 Scopus citations

Abstract

Let P ₁ ; . . . ; P _m ∈ Z[y] be any linearly independent polynomials with zero constant term. We show that there exists γ > 0 such that any subset of F _q of size at least q ^1-γ contains a nontrivial polynomial progression x,x+P ₁ (y); . . . . x+P _m (y) provided that the characteristic of F _q is large enough.

Original language	English (US)
Pages (from-to)	749-774
Number of pages	26
Journal	Duke Mathematical Journal
Volume	168
Issue number	5
DOIs	https://doi.org/10.1215/00127094-2018-0051
State	Published - Apr 1 2019

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1215/00127094-2018-0051

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abstract = " Let P 1 ; . . . ; P m ∈ Z[y] be any linearly independent polynomials with zero constant term. We show that there exists γ > 0 such that any subset of F q of size at least q 1-γ contains a nontrivial polynomial progression x,x+P 1 (y); . . . . x+P m (y) provided that the characteristic of F q is large enough.",

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AB - Let P 1 ; . . . ; P m ∈ Z[y] be any linearly independent polynomials with zero constant term. We show that there exists γ > 0 such that any subset of F q of size at least q 1-γ contains a nontrivial polynomial progression x,x+P 1 (y); . . . . x+P m (y) provided that the characteristic of F q is large enough.

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On the polynomial szemerédi theorem in finite fields

Abstract

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