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

Authors

PE Gunnells, University of Massachusetts - AmherstFollow
R Sczech

Publication Date

2003

Journal or Book Title

DUKE MATHEMATICAL JOURNAL

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.

Comments

The published version is located at http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&handle=euclid.dmj/1082744647&page=record

Pages

229-260

Volume

118

Issue

2

Recommended Citation

Gunnells, PE and Sczech, R, "Evaluation of Dedekind sums, Eisenstein cocycles, and special values of L-functions" (2003). DUKE MATHEMATICAL JOURNAL. 404.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/404