Three-term arithmetic progressions in subsets of F_q^∞ of large Fourier dimension - Fraser, Robert (Annales Fennici Mathematici, 2021)
We show that subsets of \(F_q^∞\) of large Fourier dimension must contain three-term arithmetic progressions. This contrasts with a construction of Shmerkin of a subset of \(R\) of Fourier dimension 1 with no three-term arithmetic progressions.