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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Normal forms for definite integer unimodular quadratic forms
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by Shmuel Friedland PDF
Proc. Amer. Math. Soc. 106 (1989), 917-921 Request permission

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
  • 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
  • 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, DOI 10.1007/978-1-4757-2016-7
  • John Milnor and Dale Husemoller, Symmetric bilinear forms, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 73, Springer-Verlag, New York-Heidelberg, 1973. MR 0506372
  • O. T. O’Meara, Introduction to quadratic forms, Springer-Verlag, 1963.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 106 (1989), 917-921
  • MSC: Primary 11E12
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0976366-6
  • MathSciNet review: 976366