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arXiv · 1304.0559

Perfect Lattices over Imaginary Quadratic Number Fields

Oliver Braun·Renaud Coulangeon
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Abstract

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.

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Oliver Braun, Renaud Coulangeon. 2013-04-02. Perfect Lattices over Imaginary Quadratic Number Fields. https://arxiv.org/abs/1304.0559

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