Perfect Lattices over Imaginary Quadratic Number Fields
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en
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Ce document a été publié dans
Mathematics of Computation. 2014p. 21 pages
American Mathematical Society
Résumé en anglais
We present an adaptation of Voronoi theory for imaginary quadratic number fields of class number greater than 1. This includes a characterisation of extreme Hermitian forms which is analogous to the classic characterisation ...Lire la suite >
We present an adaptation of Voronoi theory for imaginary quadratic number fields of class number greater than 1. This includes a characterisation of extreme Hermitian forms which is analogous to the classic characterisation of extreme quadratic forms as well as a version of Voronoi's famous algorithm which may be used to enumerate all perfect Hermitian forms for a given imaginary quadratic number field in dimensions 2 and 3. We also present an application of the algorithm which allows to determine generators of the general linear group of an $\O_K$-lattice.< Réduire
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