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Stable Lattices

Published online by Cambridge University Press:  20 November 2018

Harvey Cohn
Harvey Cohn*
Affiliation:
Wayne University
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The consideration of relative extrema to correspond to the absolute extremum which is the critical lattice has been going on for some time. As far back as 1873, Korkine and Zolotareff [6] worked with the ellipsoid in hyperspace (i.e., with quadratic forms), and later Minkowski [8] worked with a general convex body in two or three dimensions. They showed how to find critical lattices by selection from among a finite number of relative extrema. They were aided by the long-recognized premise that only a finite number of lattice points can enter into consideration [1] when one deals with lattices “admissible to convex bodies.”

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 261 - 270
Copyright
Copyright © Canadian Mathematical Society 1953

References

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