Lattices and packings in higher dimensions

  • Marcel BergerEmail author


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.


Modular Form Theta Function Minimal Norm Arbitrary Dimension Voronoi Cell 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Institut des Hautes Études ScientifiquesIHÉS, Bures-sur-YvetteBures-sur-YvetteFrance

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