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arXiv · 1111.1040

On the concentration of certain additive functions

Dimitris Koukoulopoulos
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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 $c>1$.

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Dimitris Koukoulopoulos. 2014-03-02. On the concentration of certain additive functions. https://doi.org/10.4064/aa162-3-2

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