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Sums of certain fractional parts

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Abstract

In this note, an upper bound for the sum of fractional parts of certain smooth functions is given. Such sums arise naturally in numerous problems of analytic number theory. The main feature is here an improvement of the main term due to the use of Weyl’s bound for exponential sums and a device used by Popov.

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Acknowledgements

The author gratefully acknowledges the anonymous referee for some corrections and remarks that have significantly improved the paper.

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  1. 2 allée de la combe, 43000, Aiguilhe, France

    Olivier Bordellès

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  1. Olivier Bordellès
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Correspondence to Olivier Bordellès.

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Bordellès, O. Sums of certain fractional parts. Period Math Hung 84, 203–210 (2022). https://doi.org/10.1007/s10998-021-00399-6

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  • DOI: https://doi.org/10.1007/s10998-021-00399-6

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