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This is a direct follow up to For which rationals is this exponential sum bounded? Given $x \in [0, 1]$, we denote by $e(x)$ the complex number $e^{2 \pi i x}$. What is the Hausdorff dimension of the ...

Let $\Omega$ be the set of all infinite binary sequences $(x_i)_{i\ge 0}$ endowed with the product topology coming from discrete topology on $\{0,1\}$. Consider $0<\alpha<1$ and let $$K_\alpha=\{...