On a class of \(\psi\)-products preserving multiplicativity. II
type: Item
instance of: scholarly article
title: On a class of \(\psi\)-products preserving multiplicativity. II
zbMATH Open document ID: 0832.11001
author: M. V. Subbarao
author: Varanasi Sitaramaiah
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1995-03-30T00:00:00Z
review text: Let \(T\) be a non-empty subset of \(\mathbb{N}\times \mathbb{N}\) and \(\psi: T\to \mathbb{N}\) a mapping satisfying conditions concerning finiteness of solutions, association and symmetry. The \(\psi\)-product of arithmetic functions \(f\), \(g\) is defined by \[ (f\psi g) (n)= \sum_{\psi (x, y)=n} f(x) g(y). \] \(\psi\) is called multiplicativity preserving if the \(\psi\)- product of multiplicative functions is again multiplicative. The authors widen the class of \(\psi\)-functions investigated in their earlier paper [Indian J. Pure Appl. Math. 22, 819-832 (1991; Zbl 0751.11006)]\ by characterizing the multiplicativity preserving functions \(\psi\) which are onto. Further they show that the arithmetic functions \(f\) which are invertible with respect to \(\psi\) form a group if \(\psi(x, y)\geq \max\{ x, y\}\) for all \((x, y)\in T\).
Mathematics Subject Classification ID: 11A25
zbMATH DE Number: 727755
zbMATH Keywords: convolution
zbMATH Keywords: product of arithmetic functions
zbMATH Keywords: multiplicitivity preserving functions
reviewed by: Thomas Maxsein
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 727755