The Universal Zeta Function for Curve Singularities and its Relation with Global Zeta Functions

Abstract

The purpose of this note is to give a brief overview on zeta functions of curve singularities and to provide some evidences on how these and global zeta functions associated to singular algebraic curves over perfect fields relate to each other.This series extends previous definitions by Galkin [12] and Green [13]. Furthermore, the Euler product formula for the formal power series yields the identity