An identity for a class of arithmetical functions of several variables

Johnson [1] evaluated the sum ∑d|n|C(d;r)|, where C(n;r) denotes Ramanujan's trigonometric sum. This evaluation has been generalized to a wide class of arithmetical functions of two variables. In this paper, we generalize this evaluation to a wide class of arithmetical functions of several vari...

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Main Author:	Pentti Haukkanen
Format:	Article
Language:	English
Published:	Hindawi Limited 1993-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	arithmetical functions of several variables multiplicative functions Ramanujan's sum and its generalizations.
Online Access:	http://dx.doi.org/10.1155/S0161171293000432

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spelling	doaj-04caaaa1bc824947a2ef0dce3b40a8612020-11-24T22:27:32ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251993-01-0116235535810.1155/S0161171293000432An identity for a class of arithmetical functions of several variablesPentti Haukkanen0Department of Mathematical Sciences, University of Tempere, P.O. Box 607, Tampere SF-33101, FinlandJohnson [1] evaluated the sum ∑d\|n\|C(d;r)\|, where C(n;r) denotes Ramanujan's trigonometric sum. This evaluation has been generalized to a wide class of arithmetical functions of two variables. In this paper, we generalize this evaluation to a wide class of arithmetical functions of several variables and deduce as special cases the previous evaluations.http://dx.doi.org/10.1155/S0161171293000432arithmetical functions of several variablesmultiplicative functionsRamanujan's sum and its generalizations.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Pentti Haukkanen
spellingShingle	Pentti Haukkanen An identity for a class of arithmetical functions of several variables International Journal of Mathematics and Mathematical Sciences arithmetical functions of several variables multiplicative functions Ramanujan's sum and its generalizations.
author_facet	Pentti Haukkanen
author_sort	Pentti Haukkanen
title	An identity for a class of arithmetical functions of several variables
title_short	An identity for a class of arithmetical functions of several variables
title_full	An identity for a class of arithmetical functions of several variables
title_fullStr	An identity for a class of arithmetical functions of several variables
title_full_unstemmed	An identity for a class of arithmetical functions of several variables
title_sort	identity for a class of arithmetical functions of several variables
publisher	Hindawi Limited
series	International Journal of Mathematics and Mathematical Sciences
issn	0161-1712 1687-0425
publishDate	1993-01-01
description	Johnson [1] evaluated the sum ∑d\|n\|C(d;r)\|, where C(n;r) denotes Ramanujan's trigonometric sum. This evaluation has been generalized to a wide class of arithmetical functions of two variables. In this paper, we generalize this evaluation to a wide class of arithmetical functions of several variables and deduce as special cases the previous evaluations.
topic	arithmetical functions of several variables multiplicative functions Ramanujan's sum and its generalizations.
url	http://dx.doi.org/10.1155/S0161171293000432
work_keys_str_mv	AT penttihaukkanen anidentityforaclassofarithmeticalfunctionsofseveralvariables AT penttihaukkanen identityforaclassofarithmeticalfunctionsofseveralvariables
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An identity for a class of arithmetical functions of several variables

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