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VOL. 49 | 2007 On $Q$-multiplicative functions having a positive upper-meanvalue
Jean-Loup Mauclaire

Editor(s) Shigeki Akiyama, Kohji Matsumoto, Leo Murata, Hiroshi Sugita

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.

Information

Published: 1 January 2007
First available in Project Euclid: 27 January 2019

zbMATH: 1193.11094
MathSciNet: MR2405606

Digital Object Identifier: 10.2969/aspm/04910219

Subjects:
Primary: 11A25
Secondary: 11N56, 11N64

Rights: Copyright © 2007 Mathematical Society of Japan

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