Computing special values of partial zeta functions

Abstract

We discuss computation of the special values of partial zeta functions associated to totally real number fields. The main tool is the \emph{Eisenstein cocycle} $\Psi $, a group cocycle for $GL_{n} (\Z )$; the special values are computed as periods of $\Psi $, and are expressed in terms of generalized Dedekind sums. We conclude with some numerical examples for cubic and quartic fields of small discriminant.