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On the concentration of certain additive functions

Volume 162 / 2014

Dimitris Koukoulopoulos Acta Arithmetica 162 (2014), 223-241 MSC: Primary 11N60, 11K65. DOI: 10.4064/aa162-3-2


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 $c>1$.


  • Dimitris KoukoulopoulosDépartement de Mathématiques et de Statistique
    Université de Montréal
    CP 6128 succ. Centre-Ville
    Montréal, Québec H3C 3J7, Canada

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