On the concentration of certain additive functions

Details On the concentration of certain additive functions On the concentration of certain additive functions

Publishing date

2011-11-04

URL

arxiv.org/abs/1111.1040v2

Science

Mathematics

Field

Number Theory

Additional info

11 pages

Type

Scientific paper

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 $f(n)=\sum_{p|n}(\log p)^{-c}$ for $c>1$.

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