Skip to main content
SpringerLink
Log in

On even unimodular positive definite quadratic lattices of rank 32

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. London: Dover 1965

    Google Scholar 

  2. Broué, M., Enguehard, M.: Une famille infinie de formes quadratiques entières; leurs groupes d'automorphismes. Ann. Scient. Éc. Norm. Sup.6, 17–52 (1973)

    Google Scholar 

  3. Conway, J.H., Pless, V.: On the Enumeration of Self-Dual codes, J. Comb. Theor., Ser. A28, 26–53 (1980)

    Google Scholar 

  4. Hecke, E.: Analytische Arithmetik der positiven quadratischen Formen, Kgl. Danske Videnskabernes Selskab. Math.-fys. Medd.17, no. 12 (1940)

  5. Leech, J., Sloane, N.J.A.: Sphere packings and error-correcting codes. Can. J. Math.23, 718–745 (1971)

    Google Scholar 

  6. Niemeier, H.-V.: Definite quadratische Formen der Discriminante 1 und Dimension 24, J. Number Theory5, 142–178 (1973)

    Google Scholar 

  7. Ozeki, M.: On Modular forms whose Fourier coefficients are non-negative integers with the constant term unity. Math. Ann.206, 187–203 (1973)

    Google Scholar 

  8. Ozeki, M.: Note on the positive definite integral quadratic lattice. J. Math. Soc. Japan28, 421–446 (1976)

    Google Scholar 

  9. Schoeneberg, B.: Das Verhalten von mehrfachen Thetareihen bei Modulsubstitutionen. Math. Ann.116, 511–523 (1939)

    Google Scholar 

  10. Siegel, C.L.: Über die Fourierschen Koeffizienten der Eisensteinschen Reihen. Danske Vid. Selskab. Mat-fys. Medd.34, No. 6 (1964)

  11. Venkov, B.B.: On the classification of integral even unimodular 24-dimensional quadratic forms. Proc. Steklov Inst. Math.148, Eng. trans. 63–74 (1980)

    Google Scholar 

  12. Venkov, B.B.: Even unimodular Euclidean lattices in dimension 32. (Russian), Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI)116, 44–55 (1982). Eng. trans. Journal of Soviet Mathematics26, 1860–1867 (1984)

    Google Scholar 

  13. Venkov, B.B.: Even unimodular Euclidean lattices of dimension 32, Part II, (Russian), Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov134, 34–58 (1984)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Liberal Arts, Nagasaki University, 1-14, Bunkyo-machi, Nagasaki, Japan

    Michio Ozeki

Authors
  1. Michio Ozeki
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ozeki, M. On even unimodular positive definite quadratic lattices of rank 32. Math Z 191, 283–291 (1986). https://doi.org/10.1007/BF01164032

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01164032

Keywords

Search

Navigation