Reciprocity laws for generalized higher dimensional Dedekind sums

• Autorzy: Robin Chapman
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 11F20: Dedekind eta function, Dedekind sums

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2000
• Tom: 93
• Numer: 2
• Strony: 189-199

Daty

wydano

2000

otrzymano

1999-08-30

Twórcy

autor

Robin Chapman

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

Bibliografia

• [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.