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VOL. 49 | 2007 On a mean value of a multiplicative function of two variables
Noboru Ushiroya

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

Abstract

We prove the existence of a mean value of arithmetical functions of two variables : $\lim_{x, y \to \infty} (xy)^{-1} \sum_{m \le x, n \le y} f(m, n)$ under some conditions, and, when $f$ is a multiplicative function of two variables, express the mean value as an infinite product over all primes. Five examples are given which are not obtained by trivial generalizations of results on arithmetical functions of one variable.

Information

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

zbMATH: 1243.11097
MathSciNet: MR2405617

Digital Object Identifier: 10.2969/aspm/04910507

Subjects:
Primary: 11N37

Rights: Copyright © 2007 Mathematical Society of Japan

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