## Advanced Studies in Pure Mathematics

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

Jean-Loup Mauclaire

#### Abstract

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

Dates
Revised: 23 January 2007
First available in Project Euclid: 27 January 2019

https://projecteuclid.org/ euclid.aspm/1548550901

Digital Object Identifier
doi:10.2969/aspm/04910219

Mathematical Reviews number (MathSciNet)
MR2405606

Zentralblatt MATH identifier
1193.11094

#### Citation

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. https://projecteuclid.org/euclid.aspm/1548550901