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Perfect lattices over imaginary quadratic number fields


Authors: Oliver Braun and Renaud Coulangeon
Journal: Math. Comp. 84 (2015), 1451-1467
MSC (2010): Primary 11H55, 11Y99; Secondary 11F06
DOI: https://doi.org/10.1090/S0025-5718-2014-02891-3
Published electronically: November 20, 2014
MathSciNet review: 3315516
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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 us to determine generators of the general linear group of an $ \mathcal {O}_K$-lattice.


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Additional Information

Oliver Braun
Affiliation: Lehrstuhl D für Mathematik, RWTH Aachen University, Templergraben 64, D-52062 Aachen, Germany
Email: oliver.braun1@rwth-aachen.de

Renaud Coulangeon
Affiliation: Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France, CNRS, IMB, UMR 5251, F-33400 Talence, France
Email: renaud.coulangeon@math.u-bordeaux1.fr

DOI: https://doi.org/10.1090/S0025-5718-2014-02891-3
Received by editor(s): January 14, 2013
Received by editor(s) in revised form: May 27, 2013, and September 9, 2013
Published electronically: November 20, 2014
Article copyright: © Copyright 2014 American Mathematical Society