Lattices and packings in higher dimensions

Marcel Berger ()
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Marcel Berger: IHÉS, Bures-sur-Yvette, Institut des Hautes Études Scientifiques

Chapter Chapter X in Geometry Revealed, 2010, pp 623-674 from Springer

Abstract: Abstract A lattice in $\mathbb{R}^3$ is a Λ that can be written as the set of integer combinations of three linearly independent vectors $\{a,b,c\}$ , say $\Lambda= \mathbb{Z} \cdot a+\mathbb{Z} \cdot b+\mathbb{Z} \cdot c$ . As in Sect. IX.4, two Euclidean invariants are immediately associated with a lattice; they are practically dictated when we seek to pack balls of like radius in the densest possible way, thus the most economical for practical life; see more in Sect. X.4.

Keywords: Modular Form; Theta Function; Minimal Norm; Arbitrary Dimension; Voronoi Cell (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-540-70997-8_10

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