Titlebook: Lectures on the Geometry of Numbers; Carl Ludwig Siegel,Komaravolu Chandrasekharan Book 1989 Springer-Verlag Berlin Heidelberg 1989 Volume

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Lecture II theory of numbers will be found in the study of points all of whose coordinates are integers. These points will be called . or .. The set of all .-points will be called a .. [See also § 5.] The following theorem about lattice points and convex bodies was proved by Minkowski.

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Lecture XIInant of the corresponding symmetric matrix.] Let .. be the minimum value of the quadratic form on the lattice of .-points excluding the origin. In the previous lecture we showed that ${r_2} leqslant sqrt {frac{{4Delta }}{3}} ,$. and the equality sign holds if and only if the form is equivalent to .

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Lecture XIInant of the corresponding symmetric matrix.] Let .. be the minimum value of the quadratic form on the lattice of .-points excluding the origin. In the previous lecture we showed that ${r_2} leqslant sqrt {frac{{4Delta }}{3}} ,$. and the equality sign holds if and only if the form is equivalent to . .

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Lecture XIVd points not belonging to .. [Notation as in § 1 of Lecture XIII.] A boundary point of . may not belong to .; for example, the zero matrix does not belong to ., yet it is a boundary point of ., because . (λ arbitrary positive) belongs to R if . does, and we may let λ tend to zero.