Computing the Zeta Function of Smooth Algebraic Curves

Abstract:

The zeta function of a curve defined over a finite field is a generating function which encodes arithmetic and geometric information about the curve. An important problem in computational number theory is to give efficient algorithms to compute zeta functions of curves. Although many algorithms have already

been developed for the computation of zeta functions for specific types of curves, they have limitations.

In this presentation, we will discuss how to compute zeta functions of smooth algebraic curves which have a plane model that has only nodes.