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Computing special values of partial zeta functions

Gautam Chinta·Paul E. Gunnells·Robert Sczech
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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} $Ψ$, a group cocycle for $GL_{n} (\Z )$; 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 cubic and quartic fields of small discriminant.

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Gautam Chinta, Paul E. Gunnells, Robert Sczech. 2000-01-03. Computing special values of partial zeta functions. https://arxiv.org/abs/math/0001011

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