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The defect of an admissible octahedron in a lattice

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Abstract

Systems of vectors determining an admissible octahedron in a lattice are considered. We discuss the property that such a system may be complemented to a basis of this lattice.

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References

  1. R. A. Rankin, “On sums of powers of linear forms, III,”Indag. Math.,10, 274–281 (1949).

    Google Scholar 

  2. H. F. Blichfeldt, “A new upper bound to the minimum value of the sum of homogeneous linear forms,”Monatsh. Math.,43, 410–414 (1936).

    MATH  Google Scholar 

  3. J. W. S. Cassels,An Introduction to the Geometry of Numbers, Cambridge Univ. Press, Cambridge (1959).

    Google Scholar 

  4. P. M. Gruber and C. G. Lekkerkerker,Geometry of Numbers, North-Holland, Amsterdam (1987).

    Google Scholar 

  5. N. M. Korobov, “On some problems in the theory of diophantine approximations,”Uspekhi Mat. Nauk [Russian Math. Surveys],22, No. 3, 83–118 (1967).

    MATH  MathSciNet  Google Scholar 

  6. T. W. Cusick and J. Wolfskill, “Lattice octahedra and sums of powers of linear forms,”J. London Math. Soc. (2),38, 207–215 (1988).

    MathSciNet  Google Scholar 

  7. N. G. Moshchevitin, “Refinement of the index bound in the octahedron problem,”Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.], No. 6 (1993).

  8. L. J. Mordell, “Lattice Octahedra,”Canad. J. Math.,12, 297–302 (1960).

    MATH  MathSciNet  Google Scholar 

  9. R. Bantegnie, “Le Problème des Octahèdres en Dimension 5,”Acta Arithm.,14, 185–202 (1968).

    MATH  MathSciNet  Google Scholar 

  10. U. Wessels,Die Sätze von White and Mordell über kritische Gitter von Polytopen in der Dimensionen 4 und 5, Preprint, Diplomarbeit, Matematisches Institut der Ruhr Universität, Bochum (1989).

    Google Scholar 

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Authors and Affiliations

  1. Moscow State University, USSR

    N. G. Moshchevitin

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  1. N. G. Moshchevitin
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Translated fromMatematicheskie Zametki, Vol. 58, No. 4, pp. 558–568, October, 1995.

The author is grateful to the French Foundation ”Pro Mathematica” for the support of the present research.

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Moshchevitin, N.G. The defect of an admissible octahedron in a lattice. Math Notes 58, 1066–1073 (1995). https://doi.org/10.1007/BF02305095

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  • DOI: https://doi.org/10.1007/BF02305095

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