BRAUN, Oliver; COULANGEON, Renaud

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BRAUN, Oliver
Lehrstuhl II für Mathematik [Aachen]

COULANGEON, Renaud
Institut de Mathématiques de Bordeaux [IMB]

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Mathematics of Computation. 2014p. 21 pages

American Mathematical Society

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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.< Leer menos

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Perfect Lattices over Imaginary Quadratic Number Fields

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