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Valuations on the ring of arithmetical functions
A. Zaharescu and M. Zaki
Received: January 18, 2007; Accepted: September 12, 2008
Abstract. In this paper we study a class of nontrivial independent absolute values on the ring A of arithmetical functions over the field C of complex numbers. We show that A is complete with respect to the metric structure obtained from each of these absolute values. We also consider an Artin-Whaples type theorem in this context.
Keywords: arithmetical functions; independent valuations.
AMS Subject classification: Primary: 13F30, 13J10.
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