On the concentration of certain additive functions

Abstract

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

arXiv comment17 pages. Final version. To appear in Acta Arith