On Jordan's generalization of Euler's function
type: Item
instance of: scholarly article
title: On Jordan's generalization of Euler's function
zbMATH Open document ID: 0942.11006
DOI: 10.1007/BF03322122
author: Jörg Schulte
published in: Results in Mathematics
publication date: 2000-01-04T00:00:00Z
review text: Let \(\alpha\) be a natural number and \(\varphi_\alpha(n)\) the number of vectors \((m_1, m_2,\dots, m_\alpha)\) with \(1\leq m_1,\dots, m_\alpha\leq n\) and \(\operatorname {gcd} (m_1,\dots, m_\alpha,n)= 1\). The case \(\alpha=1\) is Euler's \(\varphi\)-function. The author proves identities between the Jordan totients \(\varphi_\alpha\) and greatest common divisors of numbers. He explains some of the identities on finite Heisenberg groups.
Mathematics Subject Classification ID: 11A25
Mathematics Subject Classification ID: 11A05
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20K01
Mathematics Subject Classification ID: 20K25
zbMATH DE Number: 1383730
zbMATH Keywords: arithmetic functions
zbMATH Keywords: Euler's \(\varphi\)-function
zbMATH Keywords: identities
zbMATH Keywords: Jordan totients
zbMATH Keywords: greatest common divisors
zbMATH Keywords: finite Heisenberg groups
reviewed by: Jürgen Spilker
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03322122
OpenAlex ID: W2048856367
description: scientific article; zbMATH DE number 1383730