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This paper provides a probabilist point of view about some results inanalytic number theory. The main tool is the family of Zeta laws, which is aconsolation for the non-existence of an uniform law on the set of integers. Weprove the existence and compute the natural density for the pairs of coprimeintegers, and also for the pairs of coprime Gaussian integers.Along the way, werecover the decomposition of the Zeta function as an Eulerian product and somerelated results.

Les lois Z\^eta pour l'arithm\'etique