On an exponential sum related to the Möbius function

Zhang, Wei

doi:10.1090/proc/16270

On an exponential sum related to the Möbius function
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by Wei Zhang;

Proc. Amer. Math. Soc. 152 (2024), 1373-1376

DOI: https://doi.org/10.1090/proc/16270

Published electronically: August 22, 2023

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Abstract:

Let $\mu (n)$ be the Möbius 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 [J. London Math. Soc. (2) 43 (1991), pp. 193–198].

References

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