English

Three-term arithmetic progressions in subsets of $\mathbb{F}_q^{\infty}$ of large Fourier dimension

Classical Analysis and ODEs 2020-03-04 v2 Combinatorics

Abstract

We show that subsets of Fq\mathbb{F}_q^{\infty} of large Fourier dimension must contain three-term arithmetic progressions. This contrasts with a construction of Shmerkin of a subset of R\mathbb{R} of Fourier dimension 11 with no three-term arithmetic progressions.

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Cite

@article{arxiv.2002.06091,
  title  = {Three-term arithmetic progressions in subsets of $\mathbb{F}_q^{\infty}$ of large Fourier dimension},
  author = {Robert Fraser},
  journal= {arXiv preprint arXiv:2002.06091},
  year   = {2020}
}

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14 Pages