The Denef-Loeser series for toric surface singularities

Let H denote the set of formal arcs going through a singular point of an algebraic variety V defined over an algebraically closed field k of characteristic zero. In the late sixties, J. Nash has observed that for any nonnegative integer s, the set js(H) of s-jets of arcs in H is a constructible subset of some affine space. Recently (1999), J. Denef and F. Loeser have proved that the Poincaré series associated with the image of js(H) in some suitable localization of the Grothendieck ring of algebraic varieties over k is a rational function. We compute this function for normal toric surface singularities.