Perfect Lattices over Imaginary Quadratic Number Fields
Number Theory
2013-04-03 v1
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 -lattice.
Cite
@article{arxiv.1304.0559,
title = {Perfect Lattices over Imaginary Quadratic Number Fields},
author = {Oliver Braun and Renaud Coulangeon},
journal= {arXiv preprint arXiv:1304.0559},
year = {2013}
}