Advanced Studies in Pure Mathematics

On $Q$-multiplicative functions having a positive upper-meanvalue

Jean-Loup Mauclaire

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A classical approach to study properties of $Q$-multiplicative functions $f(n)$ is to associate to the mean $\frac{1}{x} \sum_{0 \le n \le x} f(n)$ the product $\prod_{0 \le j \le k} \frac{1}{q_j} \sum_{0 \le a \le q_j-1} f(aQ_j)$. We discuss its validity in the case of non-negative $Q$-multiplicative functions $f(n)$ with a positive upper meanvalue, defined via a Cantor numeration system.

Article information

Probability and Number Theory — Kanazawa 2005, S. Akiyama, K. Matsumoto, L. Murata and H. Sugita, eds. (Tokyo: Mathematical Society of Japan, 2007), 219-244

Received: 15 May 2006
Revised: 23 January 2007
First available in Project Euclid: 27 January 2019

Permanent link to this document euclid.aspm/1548550901

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11A25: Arithmetic functions; related numbers; inversion formulas
Secondary: 11N64: Other results on the distribution of values or the characterization of arithmetic functions 11N56: Rate of growth of arithmetic functions

mean-value $Q$-multiplicative functions


Mauclaire, Jean-Loup. On $Q$-multiplicative functions having a positive upper-meanvalue. Probability and Number Theory — Kanazawa 2005, 219--244, Mathematical Society of Japan, Tokyo, Japan, 2007. doi:10.2969/aspm/04910219.

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