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By considering a Moran-type construction of fractals on $[0,1]$, we show thatfor any $0\le s\le 1$, there exists some Moran fractal set, which is perfect,with Hausdorff dimension $s$ whose Fourier dimension is zero and it containsarbitrarily long arithmetic progressions.

Perfect fractal sets with zero Fourier dimension and arbitrarily long arithmetic progressions