2010 | OriginalPaper | Chapter
Lattices and Spherical Designs
Author : Gabriele Nebe
Published in: Algorithmic Number Theory
Publisher: Springer Berlin Heidelberg
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A
lattice
is a finitely generated discrete subgroup of Euclidean space. Lattices are an important algorithmic tool in number theory, integral representation theory, geometry, information theory, cryptography, crystallography and have various other applications within mathematics and beyond. Any lattice has only finitely many vectors of a given length, they form the
layers
of the lattice, which are finite subsets of spheres in the underlying Euclidean space.