Skip to main content
Log in

New bounds in some transference theorems in the geometry of numbers

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Babai, L.: On Lovász' lattice reduction and the nearest lattice point problem. Combinatorica6, 1–13 (1986)

    Google Scholar 

  2. Banaszczyk, W.: Closed subgroups of nuclear spaces are weakly closed. Studia Math.80, 119–128 (1984)

    Google Scholar 

  3. Banaszczyk, W.: Pontryagin duality for subgroups and quotients of nuclear spaces. Math. Ann.273, 653–664 (1986)

    Google Scholar 

  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. Banaszczyk, W.: Additive subgroups of topological vector spaces. (Lect. Notes Math., vol 1466) Berlin Heidelberg New York: Springer 1991

    Google Scholar 

  6. Cassels, J.W.S.: An introduction to the geometry of numbers. Berlin Göttingen Heidelberg: Springer 1959

    Google Scholar 

  7. Hastad, J.: Dual vectors and lower bounds for the nearest lattice point problem. Combinatorica8, 75–81 (1988)

    Google Scholar 

  8. Hewitt, E., Ross, K.A.: Abstract harmonic analysis, vol. II. Berlin Heidelberg New York: Springer 1970

    Google Scholar 

  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. 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. Mahler, K.: Ein Übertragungsprinzip für konvexe Körper. Čas. Péstoväní Mat. Fys.68, 93–102 (1939)

    Google Scholar 

  12. Milnor, J., Husemoller, D.: Symmetric bilinear forms. Berlin Heidelberg New York: Springer 1973

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Banaszczyk, W. New bounds in some transference theorems in the geometry of numbers. Math. Ann. 296, 625–635 (1993). https://doi.org/10.1007/BF01445125

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01445125

Mathematics Subject Classification (1991)

Navigation