On the \(\psi\)-product of D. H. Lehmer
type: Item
instance of: scholarly article
title: On the \(\psi\)-product of D. H. Lehmer
zbMATH Open document ID: 0603.10003
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1985-01-01T00:00:00Z
review text: \textit{D. H. Lehmer} [Trans. Am. Math. Soc. 33, 945-957 (1931; Zbl 0003.10202)] considered a class of multiplications defined in the set F of all arithmetic functions which obey five axioms, assuring that F becomes a commutative ring with unity with usual addition. The author notes that the exponential convolution considered by \textit{P. Erdős} and \textit{M. V. Subbarao} [Lect. Notes Math. 251, 119-125 (1972; Zbl 0228.10033)] does not obey all Lehmer's axioms and shows how to modify them so that the exponential convolution as well as many other convolutions used in number theory satisfy them.
Mathematics Subject Classification ID: 11A25
zbMATH DE Number: 3972939
zbMATH Keywords: multiplications
zbMATH Keywords: arithmetic functions
zbMATH Keywords: commutative ring with unity
zbMATH Keywords: Lehmer's axioms
zbMATH Keywords: exponential convolution
zbMATH Keywords: convolutions
author: Varanasi Sitaramaiah
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3972939