Geometry & Topology Monographs, Vol. 7 (2004),
Proceedings of the Casson Fest,
Paper no. 8, pages 205--212.

Generalized Dedekind sums

DD Long AW Reid

Abstract. Classical Dedekind sums are connected to the modular group through the construction of a (Dedekind) symbol on the cusp set of the modular group. In this paper we study generalizations of Dedekind symbols and sums that can be associated to certain Fuchsian groups uniformizing 1-punctured tori.

Keywords. Cusp set, Dedekind sum

AMS subject classification. Primary: 11F20. Secondary: 20H10.

E-print: arXiv:math.GT/0409367

Submitted to GT on 19 November 2003. (Revised 21 April 2004.) Paper accepted 20 April 2004. Paper published 19 September 2004.

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DD Long AW Reid
Department of Mathematics, University of California
Santa Barbara, CA 93106, USA
Department of Mathematics, University of Texas
Austin, TX 78712, USA

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