MOTIVIC ZETA FUNCTIONS FOR CURVE SINGULARITIES

Let X be a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristic p big enough. Given a local ring O-P,O-X at a rational singular point P of X, we attached a universal zeta function which is a rational function and admits a functional equation if O-P,O-X is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincare series attached to singular points of algebraic curves. In particular, for the local ring attached to a complex analytic function in two variables, our universal zeta function specializes to the generalized Poincare series introduced by Campillo, Delgado, and Gusein-Zade.