On the concentration of certain additive functions
Volume 162 / 2014
Acta Arithmetica 162 (2014), 223-241
MSC: Primary 11N60, 11K65.
DOI: 10.4064/aa162-3-2
Abstract
We study the concentration of the distribution of an additive function $f$ when the sequence of prime values of $f$ decays fast and has good spacing properties. In particular, we prove a conjecture by Erdős and Kátai on the concentration of $f(n)=\sum_{p|n}(\log p)^{-c}$ when $c>1$.
