English

On Davenport Expansions, Popov's formula, and Fine's query

Number Theory 2023-10-02 v3

Abstract

We establish an explicit connection between a Davenport expansion and the Popov sum. Asymptotic analysis follows as a result of these formulas. New solutions to a query of N.J. Fine are offered, and a proof of Davenport expansions is detailed.

Keywords

Cite

@article{arxiv.2004.05644,
  title  = {On Davenport Expansions, Popov's formula, and Fine's query},
  author = {Alexander E Patkowski},
  journal= {arXiv preprint arXiv:2004.05644},
  year   = {2023}
}