Higher-dimensional Dedekind sums and their bounds arising from the discrete diagonal of the n-cube

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dc.creatorBeck, Matthias
dc.creatorRobins, Sinai
dc.creatorZacks, Shelemyahu
dc.date2003-05-29
dc.date.accessioned2026-07-07T06:24:26Z
dc.date.available2026-07-07T06:24:26Z
dc.descriptionHigher-dimensional Dedekind sums are defined as a generalization of a recent 1-dimensional probability model of Dilcher and Girstmair to a d-dimensional cube. The analysis of the frequency distribution of marked lattice points leads to new formulae in certain special cases, and to new bounds for the classical Dedekind sums. Upper bounds for the generalized Dedekind sums are defined in terms of 1-dimensional moments. In the classical two-dimensional case, the ratio of these sums to their upper bounds are cosines of angles between certain vectors of n-dimensional cones, conjectured to have a largest spacial angle of pi/6.
dc.description24 pages, 8 figures
dc.identifierhttps://arxiv.org/abs/math/0305421
dc.identifierhttp://arxiv.org/abs/math/0305421
dc.identifierAdv. Appl. Math. 36, no. 1 (2006), 1-29.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96541
dc.subjectNumber Theory
dc.subject11L07
dc.titleHigher-dimensional Dedekind sums and their bounds arising from the discrete diagonal of the n-cube
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