Computing special values of partial zeta functions

Details Computing special values of partial zeta functions Computing special values of partial zeta functions

2000-01-03

arxiv.org/abs/math/0001011v1

Mathematics

Number Theory

10 pp

Scientific paper

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.

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