Three-term arithmetic progressions in subsets of F_q^∞ of large Fourier dimension

Robert Fraser

Type: Article

Publication Date: 2021-01-01

Citations: 0

DOI: https://doi.org/10.5186/aasfm.2021.4659

Abstract

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

Locations

Annales Fennici Mathematici - View - PDF

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