Computing special values of partial zeta functions

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.