2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67083We define invariants of the blow-Nash equivalence of real analytic function germs, in a similar way that the motivic zeta functions of Denef & Loeser. As a key ingredient, we extend the virtual Betti numbers, which were known for real algebraic sets, as a generalized Euler characteristics for projective constructible arc-symmetrics sets. Actually we prove more: the virtual Betti numbers are not only algebraic invariant, but also Nash-invariant of arc-symmetric sets. Our zeta functions enable to sketch the blow-Nash equivalence classes of Brieskorn polynomials of two variables.26 pages, 4 figuresAlgebraic Geometry14B05; 14P20; 14P25; 32S15text