English

Sums of certain fractional parts

Number Theory 2019-01-03 v1

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.

Keywords

Cite

@article{arxiv.1901.00170,
  title  = {Sums of certain fractional parts},
  author = {Olivier Bordellès},
  journal= {arXiv preprint arXiv:1901.00170},
  year   = {2019}
}

Comments

5 pages