JP Journal of Algebra, Number Theory and Applications
Volume 10, Issue 1, Pages 51 - 63
(February 2008)
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APPROXIMATION OF ARITHMETICAL FUNCTIONS BY EVEN FUNCTIONS
Pentti Haukkanen (Finland) and Timo Tossavainen (Finland)
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Abstract: J. Knopfmacher studied approximation of arithmetical functions of one variable using even functions. In this paper we show that this approximation can be carried out for arithmetical functions of several variables by applying even functions of several variables. We also show that this kind of approximation cannot be realized using A-even functions when A is a regular convolution other than the Dirichlet convolution. |
Keywords and phrases: arithmetical functions, even functions, Ramanujan sums, regular convolutions. |
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