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arXiv · 2002.06091

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

Robert Fraser
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Abstract

We show that subsets of $\mathbb{F}_q^{\infty}$ of large Fourier dimension must contain three-term arithmetic progressions. This contrasts with a construction of Shmerkin of a subset of $\mathbb{R}$ of Fourier dimension $1$ with no three-term arithmetic progressions.

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Robert Fraser. 2020-02-14. Three-term arithmetic progressions in subsets of $\mathbb{F}_q^{\infty}$ of large Fourier dimension. https://arxiv.org/abs/2002.06091

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