Bounded Exponential Sums with Multiplicative Coefficients

Pierre-Alexandre Bazin, Ihor Pylaiev, Fred Tyrrell

We investigate when the exponential sum $S_f(x,\hat{I}\pm ):={\sum }_{n\le x}f(n)\mathrm{e}(n\hat{I}\pm )$ is bounded, for a multiplicative function $f$ and $\hat{I}\pm \in \mathbb{R}$. We show that under natu…