Skip to main content
SpringerLink
Log in

Representations by unimodular quadratic ℤ-lattices

  • 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

  • [C] Cassels, J.W.S.: Rational quadratic forms. London New York San Francisco: Academic Press 1978

    MATH  Google Scholar 

  • [C-S] Conway, J.H., Sloane, N.J.A.: Sphere packings, lattices and groups (Grundlehren Math. Wiss., Bd. 290) Berlin Heidelberg New York: Springer 1988

    MATH  Google Scholar 

  • [D] Dolgachev, I.: Integral quadratic forms: applications to algebraic geometry. Sémin. Bourbaki, 35e année no. 611 (1982/83)

  • [J1] James, D.G.: On Witt's theorem for unimodular quadratic forms. II. Pac. J. Math.33, 645–653 (1970)

    MATH  Google Scholar 

  • [J2] James, D.G.: Representations by integral quadratic forms. J. Number Theory4, 321–329 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  • [J3] James, D.G.: Integral sums of squares in algebraic number fields. Am. J. Math.113, 129–146 (1991)

    Article  MATH  Google Scholar 

  • [J4] James, D.G.: Primitive representations by unimodular quadratic forms. J. Number Theory44, 356–366 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  • [K1] Kneser, M.: Witts Satz für quadratische Formen über lokalen Ringen. Nachr. Akad. Wiss. Gött., II. Math.-Phys. Kl. 195–203 (1972)

  • [K2] Kneser, M.: Representations of integral quadratic forms. Can. Math. Soc. Conf. Proc.4, 159–172 (1984)

    MathSciNet  Google Scholar 

  • [M-M] Miranda, R., Morrison, D.R.: The number of embeddings of integral quadratic forms. Proc. Japan Acad.61, 317–320 (1985);62, 29–32 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • [N] Nikulin, V.V.: Integral symmetric bilinear forms and some of their applications. Math. USSR Izv.14, 103–167 (1980)

    Article  MATH  Google Scholar 

  • [O'M1] O'Meara, O.T.: Quadratic forms over local fields. Am. J. Math.77, 87–116 (1955)

    Article  MATH  MathSciNet  Google Scholar 

  • [O'M2] O'Meara, O.T.: Introduction to quadratic forms (Grundlehren Math. Wiss., Bd. 117) Berlin Göttingen Heidelberg: Springer 1963

    MATH  Google Scholar 

  • [R] Riehm, C.R.: On the integral representations of quadratic forms over local fields. Am. J. Math.86, 25–62 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  • [T] Trojan, A.: The integral extension of isometries of quadratic forms over local fields. Can. J. Math.18, 920–942 (1966)

    MATH  MathSciNet  Google Scholar 

  • [U] Urabe, T.: Tie transformations of Dynkin graphs and singularities on quartic surfaces. Invent. Math.100, 207–230 (1990)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, 16802, University Park, PA, USA

    Donald G. James

Authors
  1. Donald G. James
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Dedicated to Professor Martin Kneser on his 65th birthday

This research was partially supported by the National Science Foundation

Rights and permissions

Reprints and permissions

About this article

Cite this article

James, D.G. Representations by unimodular quadratic ℤ-lattices. Math Z 215, 465–475 (1994). https://doi.org/10.1007/BF02571724

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02571724

Keywords

Search

Navigation