Three-term polynomial progressions in subsets of finite fields

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Abstract

Bourgain and Chang recently showed that any subset of Fp of density ≫p−1/15 contains a nontrivial progression x, x + y, x + y2. We answer a question of theirs by proving that if P1, P2 ∈ ℤ[y] are linearly independent and satisfy P1(0) = P2(0) = 0, then any subset of Fp of density ≫P1,P2p−1/24 contains a nontrivial polynomial progression x, x + P1(y), x + P2(y).

Original languageEnglish (US)
Pages (from-to)379-405
Number of pages27
JournalIsrael Journal of Mathematics
Volume228
Issue number1
DOIs
StatePublished - Oct 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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