# Reciprocity laws for generalized higher dimensional Dedekind sums

Acta Arithmetica (2000)

- Volume: 93, Issue: 2, page 189-199
- ISSN: 0065-1036

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topRobin Chapman. "Reciprocity laws for generalized higher dimensional Dedekind sums." Acta Arithmetica 93.2 (2000): 189-199. <http://eudml.org/doc/207409>.

@article{RobinChapman2000,

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].},

author = {Robin Chapman},

journal = {Acta Arithmetica},

keywords = {reciprocity law; higher dimensional Dedekind sums; periodic Bernoulli function},

language = {eng},

number = {2},

pages = {189-199},

title = {Reciprocity laws for generalized higher dimensional Dedekind sums},

url = {http://eudml.org/doc/207409},

volume = {93},

year = {2000},

}

TY - JOUR

AU - Robin Chapman

TI - Reciprocity laws for generalized higher dimensional Dedekind sums

JO - Acta Arithmetica

PY - 2000

VL - 93

IS - 2

SP - 189

EP - 199

AB - 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].

LA - eng

KW - reciprocity law; higher dimensional Dedekind sums; periodic Bernoulli function

UR - http://eudml.org/doc/207409

ER -

## References

top- [1] R. R. Hall, J. C. Wilson and D. Zagier, Reciprocity formulae for general Dedekind-Rademacher sums, Acta Arith. 73 (1995), 389-396. Zbl0847.11020
- [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. Zbl0920.11026
- [6] D. Zagier, Higher dimensional Dedekind sums, Math. Ann. 202 (1973), 149-172. Zbl0237.10025

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