Lattices and Spherical Designs

  • Gabriele Nebe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)


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.


Modular Form Discrete Subgroup Sphere Packing Dense Lattice Harmonic Polynomial 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Gabriele Nebe
    • 1
  1. 1.Lehrstuhl D für MathematikRWTH Aachen UniversityGermany

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