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On an exponential sum related to the Möbius function
Published 10 Apr 2022 in math.NT | (2204.04613v2)
Abstract: Let $\mu(n)$ be the M\"{o}bius function and $e(\alpha)=e{2\pi i\alpha}$. In this paper, we study upper bounds of the classical sum $$S(x,\alpha):=\sum_{1\leq n\leq x}\mu(n)e(\alpha n).$$ We can improve some classical results of Baker and Harman \cite{BH}.
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