Sums of certain fractional parts

Olivier Bordellès

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arXiv · 1901.00170

Sums of certain fractional parts

Olivier Bordellès

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Abstract

In this note, an upper bound for the sum of fractional parts of certain smooth functions is established. 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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Olivier Bordellès. 2019-01-01. Sums of certain fractional parts. https://arxiv.org/abs/1901.00170

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