We discuss computation of the special values of partial zeta functions associated to totally real number fields. The main tool is the Eisenstein cocycle Ψ, a group cocycle for GLn(Z); the special values are computed as periods of Ψ, and are expressed in terms of generalized Dedekind sums. We conclude with some numerical examples for fields of degree ≤ 5 and small discriminant.
Gautam Chinta, Paul E. Gunnells, Robert Sczech