Skip to main content

Sphere packings centered at S-units of algebraic tori

Part of the Lecture Notes in Mathematics book series (LNM,volume 1518)

Keywords

  • Class Number
  • Norm Type
  • Quadratic Extension
  • Sphere Packing
  • Global Field

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.-M. Bergé, J. Martinet, Sur un problème de dualité lié aux sphères en géometrie des nombres, J. Number Theory, 1989, v. 32, N 1, 14–42.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. J.H. Conway, N.J.A. Sloane, Sphere packings, lattices and groups, Springer, N.Y., 1988.

    CrossRef  MATH  Google Scholar 

  3. P. Deligne, Preuve des conjectures de Tate et de Shafarevitch (d'après G. Faltings), Astérisque, 1985, v. 121-122, 25–41.

    MathSciNet  MATH  Google Scholar 

  4. G.A. Kabatiansky, V.I. Levenshtein, Bounds for packing on a sphere and in space, Problemy Peredachi Informatsii, 1978, v. 14, N 1, 3–25; Engl. transl.: Problems Inform. Transmission, 1978, v. 14, Nx1, 1–17.

    MathSciNet  Google Scholar 

  5. H.K. Kim, Unit theorems on algebraic tori, Nagoya Math. J., 1988, v. 112, 117–124.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. S. Lang, Algebraic number theory, Addison — Wesley, Reading, 1970.

    MATH  Google Scholar 

  7. S.N. Litsyn, M.A. Tsfasman, Constructive high-dimensional sphere packings, Duke Math. J., 1987, v. 54, N 1, 147–161.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. J. Martinet, Tours de corps de classes et estimation de discriminants, Invent. Math., 1978, v. 44, N 1, 65–73.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. H. Minkowski, Diskontinuitätsbereich für arithmetische Aequivallenz, J. Reine Angew. Math., 1905, v. 129, 220–274.

    MathSciNet  Google Scholar 

  10. T. Ono, On some arithmetic properties of linear algebraic groups, Ann. of Math., 1959, v. 70, N 2, 266–290.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. T. Ono, Arithmetic of algebraic tori, Ann. of Math., 1961, v. 74, N 1, 101–139.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. M. Ju. Rosenbloom, M.A. Tsfasman, Multiplicative lattices in global fields, Invent. Math., 1990, v. 101, N 3, 687–696.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. A. Schinzel, On the product of the conjugates outside the unit circle of an algebraic number, Acta Arith., 1973, v. 24, 385–399; 1975, v. 26, 329–331.

    MathSciNet  MATH  Google Scholar 

  14. P. Schneider, Iwasawa L-functions of varieties over algebraic number fields. A first approach, Invent. Math., 1983, v. 71, N 2, 251–293.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. J.-M. Shyr, A generalization of Dirichlet's unit theorem, J. Number Theory, 1977, v. 9, N 2, 213–217.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. J.-M. Shyr, On some class number relations of algebraic tori, Mich. Math. J., 1977, v. 24, N 3, 365–377.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. J.-M. Shyr, Class numbers of binary quadratic forms over algebraic number fields, J. Reine Angew. Math., 1979, v. 307–308, 353–364.

    MathSciNet  MATH  Google Scholar 

  18. M.A.Tsfasman, Global fields, codes and sphere packings, Preprint, 1989.

    Google Scholar 

  19. S.G. VlĂduţ, V.G. Drinfeld, Number of points on an algebraic curve, Funktsional. Anal. i Prilozhen., 1983, v. 17, N 1, 68–69; Engl. transl.: Functional Anal. Appl., 1983, v. 17, N 1, 53–54.

    CrossRef  MathSciNet  Google Scholar 

  20. V.E. Voskresenskii, Algebraic tori, Nauka, Moscow, 1977 (Russian).

    MATH  Google Scholar 

  21. V.E. Voskresenskii, The arithmetic of algebraic groups and homogeneous spaces, Studies in Number Theory. Algebraic Number Theory. Saratov Univ. Press, 1987, 7–38; Engl. transl: Selecta Math. Soviet., 1990, v.9, N 1, 22–48.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1992 Springer-Verlag

About this paper

Cite this paper

Kunyavskii, B.È. (1992). Sphere packings centered at S-units of algebraic tori. In: Stichtenoth, H., Tsfasman, M.A. (eds) Coding Theory and Algebraic Geometry. Lecture Notes in Mathematics, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087996

Download citation

  • DOI: https://doi.org/10.1007/BFb0087996

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55651-0

  • Online ISBN: 978-3-540-47267-4

  • eBook Packages: Springer Book Archive