English

On the concentration of certain additive functions

Number Theory 2017-06-12 v4

Abstract

We study the concentration of the distribution of an additive function, when the sequence of prime values of ff decays fast and has good spacing properties. In particular, we prove a conjecture by Erdos and Katai on the concentration of f(n)=pn(logp)cf(n)=\sum_{p|n}(\log p)^{-c} when c>1c>1.

Keywords

Cite

@article{arxiv.1111.1040,
  title  = {On the concentration of certain additive functions},
  author = {Dimitris Koukoulopoulos},
  journal= {arXiv preprint arXiv:1111.1040},
  year   = {2017}
}

Comments

17 pages. Final version. To appear in Acta Arith

R2 v1 2026-06-21T19:30:50.807Z