On \(p\)- and \(q\)-additive functions
type: Item
instance of: scholarly article
title: On \(p\)- and \(q\)-additive functions
zbMATH Open document ID: 0958.11054
author: Yoshihisa Uchida
published in: Tokyo Journal of Mathematics
publication date: 2001-04-10T00:00:00Z
review text: The paper attempts to describe those arithmetic functions that are simultaneously \(p\)- and \(q\)-additive for two integers \(p, q\) which are not powers of a common integer. It is proved that the function is a sum of a linear and a periodic function, whose period is of the form \((p^l, q^m)\). In particular, if \(p,q\) are coprime, the function must be linear. A similar result is given for \(p\)- and \(q\)-multiplicative functions. These results extend those of \textit{T. Toshimitsu} [Tokyo J. Math. 21, 107-113 (1998; Zbl 0906.11036)], where strongly \(q\)-additive and multiplicative functions were considered.
Mathematics Subject Classification ID: 11K65
zbMATH DE Number: 1340489
zbMATH Keywords: \(q\)-additivity
zbMATH Keywords: arithmetic functions
reviewed by: Imre Z. Ruzsa
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270041614
OpenAlex ID: W2067188185
DOI: 10.3836/TJM/1270041614
description: scientific article; zbMATH DE number 1340489