Geodesic
Valuations on the ring of arithmetical functions
Acta mathematica Universitatis Comenianae, Tome 78 (2009) no. 1 
A. Zaharescu; M. Zaki. Valuations on the ring of arithmetical functions. Acta mathematica Universitatis Comenianae, Tome 78 (2009) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2009_78_1_a12/
@article{AMUC_2009_78_1_a12,
     author = {A. Zaharescu and M. Zaki},
     title = {Valuations on the ring of arithmetical functions},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2009},
     volume = {78},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2009_78_1_a12/}
}
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Voir la notice de l'article provenant de la source Comenius University

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.