Zeta functions and blow-Nash equivalence
We propose a refinement of the notion of blow-Nash equivalence between Nash function germs, which has been introduced in  as an analog in the Nash setting of the blow-analytic equivalence defined by T.-C. Kuo . The new definition is more natural and geometric. Moreover, this equivalence relation still does not admit moduli for a Nash family of isolated singularities. But though the zeta functions constructed in  are no longer invariants for this new relation, thanks to a Denef & Loeser formula coming from motivic integration in a Nash setting, we manage to derive new invariants for this equivalence relation.