English

On Ramanujan smooth expansions for a general arithmetic function

Number Theory 2024-07-30 v1

Abstract

We study in detail the Ramanujan smooth expansions, for arithmetic functions; we start with the most general ones, for which we supply the "PP-local expansions", for arguments with all prime-factors pPp\le P (namely, PP-smooth arguments), that are also square-free; then, we supply general results for interesting subsets of arithmetic functions, regarding both their PP-local and (global) Ramanujan smooth expansions.

Keywords

Cite

@article{arxiv.2407.19759,
  title  = {On Ramanujan smooth expansions for a general arithmetic function},
  author = {Giovanni Coppola},
  journal= {arXiv preprint arXiv:2407.19759},
  year   = {2024}
}

Comments

Plain TeX, 20 pages, plus 1 p.bib

R2 v1 2026-06-28T17:56:28.022Z