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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 ...

Given $x \in [0, 1]$, we denote by $e(x)$ the complex number $e^{2 \pi i x}$. Can we characterise the set of rationals $x$ for which the sum $$A_N(x)\, :=\, \sum_{n = 0}^N e(2^n x)$$ remains bounded ...

Given a sequence $a_n$ (of real numbers, described more fully below), one may define the exponential generating function (on the complex plane) as $E(z)=\sum_{n=0}^\infty a_n z^n/n!$. The derivatives $...