Motivic Zeta Functions for Curve Singularities

J. J. Moyano-Fernandez, W. A. Zuniga-Galindo

Published 2009-03-06, updated 2009-08-28Version 3

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,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,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.