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

Authors

  • Robert Fraser University of Edinburgh, School of Mathematics

Keywords:

Fourier dimension, three-term arithmetic progressions, Fourier analysis, additive combinatorics

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.

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Published

2021-08-20

Issue

Vol. 46 No. 2 (2021)

Section

Articles

License

Copyright (c) 2021 The Finnish Mathematical Society

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Fraser, R. (2021). Three-term arithmetic progressions in subsets of F_q^∞ of large Fourier dimension. Annales Fennici Mathematici, 46(2), 1007-1030. https://afm.journal.fi/article/view/110939