p. 115 - 119 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. PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2009, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |