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- W2121695760 abstract "George 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 anely equivalent. Delaunay (1937-38) asked about possible relative volumes of lattice Delaunay simplexes. We construct an innite series of Delaunay simplexes of relative volume n 3, the best known as of now. This series gives rise to an inntie series of perfect forms with remarkable properties: e.g. 5 D5; 6 E 6 ; 7 ’ 7 ; for all n the domain of n is adjacent to the domain of the 2-nd perfect form Dn: Perfect form n is a direct n-dimensional generalization of Korkine and Zolotare’s 3-rd perfect form 5 in 5 variables. We prove that n is equivalent to Anzin’s (1991) form hn." @default.
- W2121695760 created "2016-06-24" @default.
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- W2121695760 date "2001-12-11" @default.
- W2121695760 modified "2023-09-27" @default.
- W2121695760 title "An Infinite Series of Perfect Quadratic Forms and Big Delaunay Simplexes in Z^n" @default.
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