Coverings, Lattices and Quantizers

  • J. H. Conway
  • N. J. A. Sloane
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 290)


This second chapter continues the description of the questions motivating this book. We first discuss the problem of finding the best covering of space by overlapping spheres, a kind of dual to the packing problem. Then we introduce the language of quadratic forms, show that lattices and quadratic forms are really the same, and explain the connections with number theory. One of the central issues is the classification of integral quadratic forms or lattices. The last section describes the problem of designing good quantizers or analog-to-digital converters. For each problem we summarize what is presently known about its solution.


Quadratic Form Modular Form Hexagonal Lattice Voronoi Cell Theta Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • J. H. Conway
  • N. J. A. Sloane

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