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 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.

• Type: Conference
• Year: 2000
• Where: ANTS
• Authors: Gautam Chinta, Paul E. Gunnells, Robert Sczech
• Keywords: Algorithms, ANTS 2000, Generalized Dedekind Sums, Partial Zeta Functions, Special Values