An Infinite Series of Perfect Quadratic Forms and Big Delaunay Simplexes in Z^n

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dc.creatorErdahl, Robert
dc.creatorRybnikov, Konstantin
dc.date2001-12-11
dc.date.accessioned2026-07-07T04:45:09Z
dc.date.available2026-07-07T04:45:09Z
dc.descriptionGeorge Voronoi (1908-09) introduced two important reduction methods for positive quadratic forms: the reduction with perfect forms, and the reduction with L-type domains. A form is perfect if can be reconstructed from all representations of its arithmetic minimum. Two forms have the same L-type if Delaunay tilings of their lattices are affinely equivalent. Delaunay (1937-38) asked about possible relative volumes of lattice Delaunay simplexes. We construct an infinite series of Delaunay simplexes of relative volume n-3, the best known as of now. This series gives rise to a new infintie series of perfect forms TF_{n} with interesting properties, e.g. TF_{5}=D_{5}, TF_{6}=E*_{6}, TF_{7}=ϕ_{15}^{7}. For all n the domain of TF_{n} is adjacent to the domain of the 2-nd perfect form D_{n}. Perfect form TF_{n} is a direct n-dimensional generalization of Korkine and Zolotareff's 3-rd perfect form ϕ_{2}^{5} in 5 variables. It is likely that this form is equivalent to Anzin's (1991) form h_n.
dc.descriptionshort version
dc.identifierhttps://arxiv.org/abs/math/0112098
dc.identifierhttp://arxiv.org/abs/math/0112098
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62860
dc.subjectMetric Geometry
dc.subjectNumber Theory
dc.subject52,11
dc.titleAn Infinite Series of Perfect Quadratic Forms and Big Delaunay Simplexes in Z^n
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