ArticleOriginal scientific text

Title

Reciprocity laws for generalized higher dimensional Dedekind sums

Authors 1

Affiliations

  1. Division of Information and Communication Sciences, Macquarie University, Sydney, New South Wales 2109, Australia

Abstract

We define a class of generalized Dedekind sums and prove a family of reciprocity laws for them. These sums and laws generalize those of Zagier [6]. The method is based on that of Solomon [5].

Bibliography

  1. R. R. Hall, J. C. Wilson and D. Zagier, Reciprocity formulae for general Dedekind-Rademacher sums, Acta Arith. 73 (1995), 389-396.
  2. H S. Hu, Shintani cocycles and generalized Dedekind sums, Ph.D. thesis, Univ. of Pennsylvania, 1997.
  3. S. Hu and D. Solomon, Properties of higher-dimensional Shintani generating functions and cocycles on PGL₃(ℚ), Proc. London Math. Soc., to appear.
  4. H. Rademacher, Generalization of the reciprocity formula for Dedekind sums, Duke Math. J. 21 (1954), 391-397.
  5. D. Solomon, Algebraic properties of Shintani's generating functions: Dedekind sums and cocycles on PGL₂(ℚ), Compositio Math. 112 (1998), 333-362.
  6. D. Zagier, Higher dimensional Dedekind sums, Math. Ann. 202 (1973), 149-172.
Pages:
189-199
Main language of publication
English
Received
1999-08-30
Published
2000
Exact and natural sciences