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The minimum and the primitive representation of positive definite quadratic forms II

Published online by Cambridge University Press:  22 January 2016

Yoshiyuki Kitaoka
Yoshiyuki Kitaoka*
Affiliation:
Graduate School of Polymathematics, Nagoya University, Chikusa-ku, Nagoya 464-01, Japan
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We are concerned with representation of positive definite quadratic forms by a positive definite quadratic form. Let us consider the following assertion

Am, n : Let M, N be positive definite quadratic lattices over Z with rank(M) = m and rank(N) = n respectively. We assume that the localization Mp is represented by Np for every prime p, that is there is an isometry from Mp to Np. Then 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 141 , March 1996 , pp. 1 - 27
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

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