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 of large Fourier dimension must contain three-term arithmetic progressions. This contrasts with a construction of Shmerkin of a subset of of Fourier dimension with no three-term arithmetic progressions.
Keywords
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