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Local minima of lattices and vertices of Klein polyhedra

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Functional Analysis and Its Applications Aims and scope

Abstract

We prove that each vertex of a Klein polyhedron of a lattice is a local minimum.

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References

  1. F. Klein, Nachr. Ges. Wiss. Göttingen, No. 3, 357–359 (1895).

  2. G. F. Voronoi, Collected Papers [in Russian], Vol. 1, Academy of Sciences of the Ukrainian SSR Press, Kiev, 1952.

    Google Scholar 

  3. H. Minkowski, Ann. Sci. École Norm. Sup., Ser. 3, 13, No. 2, 41–60 (1896).

    MATH  MathSciNet  Google Scholar 

  4. V. I. Arnold, Continued Fractions [in Russian], MCCME, Moscow, 2000.

    Google Scholar 

  5. J. W. S. Cassels, An Introduction to the Geometry of Numbers, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959.

    Google Scholar 

  6. J. W. S. Cassels, An Introduction to Diophantine Approximation, Cambridge University Press, New York, 1957.

    Google Scholar 

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Authors and Affiliations

  1. Khabarovsk Branch of the Institute of Applied Mathematics, Russia

    V. A. Bykovskii

  2. Far East Branch of the Russian Academy of Sciences, Russia

    V. A. Bykovskii

Authors
  1. V. A. Bykovskii
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__________

Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 40, No. 1, pp. 69–71, 2006

Original Russian Text Copyright © by V. A. Bykovskii

Supported by RFBR grant No. 04-01-97000 and INTAS grant No. 03-51-5070.

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Bykovskii, V.A. Local minima of lattices and vertices of Klein polyhedra. Funct Anal Its Appl 40, 56–57 (2006). https://doi.org/10.1007/s10688-006-0007-2

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  • DOI: https://doi.org/10.1007/s10688-006-0007-2

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