Binary Hermitian Lattices over Number Fields

DOI10.1080/10586458.2019.1618756zbMath1493.11081OpenAlexW3093660145WikidataQ127728321 ScholiaQ127728321MaRDI QIDQ5070656

Gabriele Nebe, Markus Kirschmer

Publication date: 14 April 2022

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10586458.2019.1618756

zbMATH Keywords

binary Hermitian formsclass numbersclassification algorithmorders in quaternion algebrasgenera of latticesHermitian lattices over CM-fields

Mathematics Subject Classification ID

General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Quadratic forms over global rings and fields (11E12) Class numbers of quadratic and Hermitian forms (11E41) Quaternion and other division algebras: arithmetic, zeta functions (11R52)

Uses Software

• Magma

Cites Work

• A fourth extremal even unimodular lattice of dimension 48
• Automorphisms of extremal unimodular lattices in dimension 72
• Optimality and uniqueness of the Leech lattice among lattices
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• Some cyclo-quaternionic lattices
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• Arithmetic of unitary groups
• Definite quadratische Formen der Dimension 24 und Diskriminante 1
• ON AUTOMORPHISMS OF EXTREMAL EVEN UNIMODULAR LATTICES
• Corrigendum: Algorithmic Enumeration of Ideal Classes for Quaternion Orders
• Lattices and Codes
• Improved Methods for Calculating Vectors of Short Length in a Lattice, Including a Complexity Analysis
• Zur Zahlentheorie der Quaternionen-Algebren.
• Simplification pour les ordres des corps de quaternions totalement définis.
• Finite quaternionic matrix groups
• An even unimodular 72-dimensional lattice of minimum 8
• Some Sphere Packings in Higher Space
• A Group of Order 8,315,553,613,086,720,000
• Integral representations of hermitian forms over local fields.
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