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Generalized Dedekind sums

Darren D Long and Alan W Reid

Geometry & Topology Monographs 7 (2004) 205–212

DOI: 10.2140/gtm.2004.7.205
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.

Dedicated to Andrew Casson on the occasion of his 60th birthday
Keywords

Cusp set, Dedekind sum
Mathematical Subject Classification

Primary: 11F20

Secondary: 20H10
References
Publication

Received: 19 November 2003
Revised: 21 April 2004
Accepted: 20 April 2004
Published: 19 September 2004
Authors
Darren D Long
Department of Mathematics
University of California
Santa Barbara CA 93106
USA
Alan W Reid
Department of Mathematics
University of Texas
Austin TX 78712
USA