Evaluation of Dedekind sums, Eisenstein cocycles, and special values of L-functions

Preprint

5 October 1999

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/9909141

Abstract

We define certain higher-dimensional Dedekind sums that generalize the classical Dedekind-Rademacher sums, and show how to compute them effectively using a generalization of the continued-fraction algorithm. We present two applications. First, we show how to express special values of partial zeta functions associated to totally real number fields in terms of these sums via the Eisenstein cocycle introduced by the second author. Hence we obtain a polynomial-time algorithm for computing these special values. Second, we show how to use our techniques to compute certain special values of the Witten zeta-function, and compute some explicit examples.

Keywords

EISENSTEIN COCYCLES
CONTINUED FRACTION
SPECIAL VALUES
ZETA FUNCTIONS
DEDEKIND SUMS
ALGORITHM

All Related Versions

Version 1, 1999-09-23, ArXiv
Version 2, 1999-10-05, ArXiv

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