1 June 2003 Evaluation of Dedekind sums, Eisenstein cocycles, and special values of L-functions
Paul E. Gunnells, Robert Sczech
Duke Math. J. 118(2): 229-260 (1 June 2003). DOI: 10.1215/S0012-7094-03-11822-0

Abstract

We define higher-dimensional Dedekind sums that generalize the classical Dedekind-Rademacher sums as well as Zagier's sums, and we 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 R. Sczech. 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 we compute some explicit examples.

Citation

Download Citation

Paul E. Gunnells. Robert Sczech. "Evaluation of Dedekind sums, Eisenstein cocycles, and special values of L-functions." Duke Math. J. 118 (2) 229 - 260, 1 June 2003. https://doi.org/10.1215/S0012-7094-03-11822-0

Information

Published: 1 June 2003
First available in Project Euclid: 23 April 2004

zbMATH: 1047.11041
MathSciNet: MR1980994
Digital Object Identifier: 10.1215/S0012-7094-03-11822-0

Subjects:
Primary: 11F20
Secondary: 11F75 , 11R42

Rights: Copyright © 2003 Duke University Press

Vol.118 • No. 2 • 1 June 2003
Back to Top