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A structure theorem for a pair of quadratic forms


Authors: J. S. Hsia, M. Jöchner and Y. Y. Shao
Journal: Proc. Amer. Math. Soc. 119 (1993), 731-734
MSC: Primary 11E12
DOI: https://doi.org/10.1090/S0002-9939-1993-1155599-3
MathSciNet review: 1155599
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Abstract: For any two lattices $ L$ and $ K$ in the same genus there exist isometric primitive sublattices $ {L'},{K'}$ of codimension $ 1$. This result not only proves Friedland's conjecture but also extends it to lattices in an arbitrary genus and defined over any algebraic number field.


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

  • [BH] J. W. Benham and J. S. Hsia, Spinor equivalence of quadratic forms, J. Number Theory 17 (1983), 337-342. MR 724532 (85f:11024)
  • [F] S. Friedland, Normal forms for definite integer unimodular quadratic forms, Proc. Amer. Math. Soc. 106 (1989), 917-921. MR 976366 (90h:11031)
  • [HKK] J. S. Hsia, Y. Kitaoka, and M. Kneser, Representations of positive definite quadratic forms, J. Reine Angew. Math. 301 (1978), 132-141. MR 0560499 (58:27758)

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DOI: https://doi.org/10.1090/S0002-9939-1993-1155599-3
Article copyright: © Copyright 1993 American Mathematical Society

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