In this paper we investigate the ring Ar(R) of arithmetical functions in r variables over an integral domain R. We study a class of absolute values, and a class of derivations on Ar(R). We show that a certain extension of Ar(R) is a discrete valuation ring. We also investigate the metric structure of the ring Ar(R).
In this paper, we present some identities involving convolutions of Dirichlet characters and the Möbius function, which are related to a well known identity of Ramanujan, Hardy and Littlewood.
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