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Representations of quadratic forms

Published online by Cambridge University Press:  22 January 2016

Yoshiyuki Kitaoka
Yoshiyuki Kitaoka*
Affiliation:
Department of Mathematics, Nagoya University
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We have shown in [1]

Theorem A. Let L be a lattice in a regular quadratic space U over Q; then L has a submodule M satisfying the following conditions 1),2):

  • 1) dM ≠ 0, rank M = rank L — 1, and M is a direct summand of L as a module.

  • 2) Let L′ be a lattice in some regular quadratic space U′ over Q satisfying dL′ = dL, rank L′ — rank L, tp(L′) ≥ tp(L) for any prime p. If there is an isometry α from M into L′ such that α(M) is a direct summand of L′ as a module, then L′ is isometric to L.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 69 , February 1978 , pp. 117 - 120
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1978

References

[1] Kitaoka, Y., Representations of quadratic forms and their application to Selberg’s zeta functions, Nagoya Math. J. vol. 63 (1976), 153–162.Google Scholar
[2] O’Meara, O. T., Introduction to quadratic forms, Springer-Verlag, 1963.CrossRefGoogle Scholar