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The minimum and the primitive representation of positive definite quadratic forms

Published online by Cambridge University Press:  22 January 2016

Yoshiyuki Kitaoka
Yoshiyuki Kitaoka*
Affiliation:
Department of Mathematics, Nagoya University, Chikusa-ku Nagoya 464-01, Japan
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Let M, N be positive definite quadratic lattices over Z with rank(M) = m and rank(N) = n respectively. When there is an isometry from M to N, we say that M is represented by N (even in the local cases). In the following, we assume that the localization Mp is represented by Np for every prime p. Let us consider the following assertion Am,n(N):

Am,n(N): There exists a constant c(N) dependent only on N so that M is represented by N if min(M) > c(N), where min(M) denotes the least positive number represented by M.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 133 , March 1994 , pp. 127 - 153
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

References

[1] Hsia, J. S., Kitaoka, Y. and Kneser, M., Representations of positive definite quadratic forms, J. reine angew. Math., 301 (1978), 132–141.Google Scholar
[2] Kitaoka, Y., “Lectures on Siegel modular forms and representation by quadratic forms,” Springer-Verlag, Heidelberg, 1986.CrossRefGoogle Scholar
[3] Kitaoka, Y., Local densities of quadratic forms, in “Investigations in Number theory (Advanced Studies in Pure Math.),” 1987 pp. 433–460.Google Scholar
[4] Kitaoka, Y., Some remarks on representations of positive definite quadratic forms, Nagoya Math. J., 115(1989), 23–41.CrossRefGoogle Scholar
[5] Kitaoka, Y., “Arithmetic of quadratic forms,” Cambridge University Press, 1993.CrossRefGoogle Scholar
[6] O’Meara, O. T., “Introduction to quadratic forms,” Springer-Verlag, 1963.CrossRefGoogle Scholar