Perfect Lattices over Imaginary Quadratic Number Fields

2013/04/02 by Braun, Oliver, Coulangeon, Renaud
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1304.0559

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 Ø_K-lattice.

Related

• Perfect Forms over Imaginary Quadratic Fields
• An algorithm for g-invariant on unary Hermitian lattices over imaginary quadratic fields
• Binary normal regular Hermitian lattices over imaginary quadratic fields
• Even universal binary Hermitian lattices over imaginary quadratic fields
• Extremality and designs in spaces of quadratic forms