English

A Generalized Davenport Expansion

Number Theory 2021-10-26 v2

Abstract

We prove a new generalization of Davenport's Fourier expansion of the infinite series involving the fractional part function over arithmetic functions. A new Mellin transform related to the Riemann zeta function is also established.

Keywords

Cite

@article{arxiv.2005.08279,
  title  = {A Generalized Davenport Expansion},
  author = {Alexander E Patkowski},
  journal= {arXiv preprint arXiv:2005.08279},
  year   = {2021}
}

Comments

Corrected the first version

R2 v1 2026-06-23T15:36:23.054Z