Advertisement

Mathematische Annalen

, Volume 296, Issue 1, pp 625–635 | Cite as

New bounds in some transference theorems in the geometry of numbers

  • W. Banaszczyk
Article

Mathematics Subject Classification (1991)

11H06 11H60 52C07 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Babai, L.: On Lovász' lattice reduction and the nearest lattice point problem. Combinatorica6, 1–13 (1986)Google Scholar
  2. 2.
    Banaszczyk, W.: Closed subgroups of nuclear spaces are weakly closed. Studia Math.80, 119–128 (1984)Google Scholar
  3. 3.
    Banaszczyk, W.: Pontryagin duality for subgroups and quotients of nuclear spaces. Math. Ann.273, 653–664 (1986)Google Scholar
  4. 4.
    Banaszczyk, W.: Polar lattices from the point of view of nuclear spaces. Rev. Mat. Univ. Complutense Madr.2 (special issue), 35–46 (1989)Google Scholar
  5. 5.
    Banaszczyk, W.: Additive subgroups of topological vector spaces. (Lect. Notes Math., vol 1466) Berlin Heidelberg New York: Springer 1991Google Scholar
  6. 6.
    Cassels, J.W.S.: An introduction to the geometry of numbers. Berlin Göttingen Heidelberg: Springer 1959Google Scholar
  7. 7.
    Hastad, J.: Dual vectors and lower bounds for the nearest lattice point problem. Combinatorica8, 75–81 (1988)Google Scholar
  8. 8.
    Hewitt, E., Ross, K.A.: Abstract harmonic analysis, vol. II. Berlin Heidelberg New York: Springer 1970Google Scholar
  9. 9.
    Khinchin, A.I.: A quantitative formulation of Kronecker's theory of approximation. Izv. Akad. Nauk SSSR, Ser. Mat.12, 113–122 (1948)Google Scholar
  10. 10.
    Lagarias, J.C., Lenstra, H.W., Schnorr, C.P.: Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice. Combinatorica10, 333–348 (1990)Google Scholar
  11. 11.
    Mahler, K.: Ein Übertragungsprinzip für konvexe Körper. Čas. Péstoväní Mat. Fys.68, 93–102 (1939)Google Scholar
  12. 12.
    Milnor, J., Husemoller, D.: Symmetric bilinear forms. Berlin Heidelberg New York: Springer 1973Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • W. Banaszczyk
    • 1
  1. 1.Institute of MathematicsŁódź UniversityŁódźPoland

Personalised recommendations