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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

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[6] O’Meara, O. T., “Introduction to quadratic forms,” Springer-Verlag, 1963.CrossRefGoogle Scholar