Properties of rational arithmetic functions

Vichian Laohakosol and Nittiya Pabhapote

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-21

Abstract:

Rational arithmetic functions are arithmetic functions of the form g 1 ∗ ⋯ ∗ g r ∗ h 1 − 1 ∗ ⋯ ∗ h s − 1 , where g i , h j are completely multiplicative functions and ∗ denotes the Dirichlet convolution. Four aspects of these functions are studied. First, some characterizations of such functions are established; second, possible Busche-Ramanujan-type identities are investigated; third, binomial-type identities are derived; and finally, properties of the Kesava Menon norm of such functions are proved.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:175048

DOI: 10.1155/IJMMS.2005.3997

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