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Scalar extension of quadratic lattices II
Published online by Cambridge University Press: 22 January 2016
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Let k be a totally real algebraic number field, the maximal order of k, and let L (resp. M) be a Z-lattice of a positive definite quadratic space U (resp. V) over the field Q of rational numbers. Suppose that there is an isometry σ from
L onto
M. We have shown that the assumption implies σ(L) = M in some cases in [2]. Our aim in this paper is to improve the results of [2]. In § 1 we introduce the notion of E-type: Let L be a positive definite quadratic lattice over Z.
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- Research Article
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1977
References
[1]
Blichfeldt, H. F., The minimum value of quadratic forms, and the closest packing of spheres, Math. Ann., 101 (1929), 605–608.Google Scholar
[2]
Kitaoka, Y., Scalar extension of quadratic lattices, Nagoya Math. J., 66 (1977), 139–149.Google Scholar
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