PORTUGALIAEMATHEMATICA
Vol. 56, No. 3, pp. 329-343 (1999)
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PORTUGALIAE MATHEMATICA Vol. 56, No. 3, pp. 329-343 (1999) |
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Rational Arithmetical Functions of Order (2,1) with Respect to Regular ConvolutionsPentti HaukkanenDepartment of Mathematical Sciences, University of Tampere,P.O. Box 607, FIN-33101 Tampere - FINLAND Abstract: S.S. Pillai's arithmetical function $P(n)=\sum_{m\ppmod n}(m,n)$ is an example of a rational arithmetical function of order $(2,1)$. We generalize $P(n)$ with respect to Narkiewicz's regular convolution and show that the generalized Pillai's function is an example of a rational arithmetical function of order $(2,1)$ with respect to Narkiewicz's regular convolution. We derive identities for rational arithmetical functions of order $(2,1)$ with respect to Narkiewicz's regular convolution and therefore also for Pillai's function and its generalization. Keywords: Rational arithmetical functions; Narkiewicz's regular convolution; Pillai's function; identical equations. Classification (MSC2000): 11A25. Full text of the article:
Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.
© 1999 Sociedade Portuguesa de Matemática
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