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Number Theory pp 327-362 | Cite as

The Geometry of Numbers

  • W. A. Coppel
Chapter
Part of the Universitext book series (UTX)

Abstract

Minkowski (1891) found a new and more geometric proof of Hermite’s result, which gave a much smaller value for the constant c n . Soon afterwards (1893) he noticed that his proof was valid not only for an n-dimensional ellipsoid f (x) ≤ const., but for any convex body which was symmetric about the origin. This led him to a large body of results, to which he gave the somewhat paradoxical name ‘geometry of numbers’. It seems fair to say that Minkowski was the first to realize the importance of convexity for mathematics, and it was in his lattice point theorem that he first encountered it.

Keywords

Root Lattice Convex Body Voronoi Cell Nonempty Interior Lattice Packing 
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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Additional References

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • W. A. Coppel
    • 1
  1. 1.GriffithAustralia

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