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Normal forms for definite integer unimodular quadratic forms

Author: Shmuel Friedland
Journal: Proc. Amer. Math. Soc. 106 (1989), 917-921
MSC: Primary 11E12
MathSciNet review: 976366
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Abstract: In this paper we show that any two positive definite integer unimodular quadratic forms have a common sublattice of codimension 2. Moreover, any such form is equivalent to a semi-normal form with at most three eigenvalues different from 1.

References [Enhancements On Off] (What's this?)

  • [Cas] J. W. S. Cassels, Rational quadratic forms, London Mathematical Society Monographs, vol. 13, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], London-New York, 1978. MR 522835
  • [C-S] J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 290, Springer-Verlag, New York, 1988. With contributions by E. Bannai, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. MR 920369
  • [M-H] John Milnor and Dale Husemoller, Symmetric bilinear forms, Springer-Verlag, New York-Heidelberg, 1973. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 73. MR 0506372
  • [Ome] O. T. O'Meara, Introduction to quadratic forms, Springer-Verlag, 1963.

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Article copyright: © Copyright 1989 American Mathematical Society

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