On the polynomial szemerédi theorem in finite fields

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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 languageEnglish (US)
Pages (from-to)749-774
Number of pages26
JournalDuke Mathematical Journal
Issue number5
StatePublished - Apr 1 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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