Abstract
Consider an arbitrary positive-definite quadratic form in n variables with determinant Δ. [By the determinant of a quadratic form is meant the determinant of the corresponding symmetric matrix.] Let r n be the minimum value of the quadratic form on the lattice of g-points excluding the origin. In the previous lecture we showed that ${r_2} \leqslant \sqrt {\frac{{4\Delta }}{3}} ,$
and the equality sign holds if and only if the form is equivalent to
.
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© 1989 Springer-Verlag Berlin Heidelberg
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Siegel, C.L., Chandrasekharan, K. (1989). Lecture XII. In: Lectures on the Geometry of Numbers. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-08287-4_12
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DOI: https://doi.org/10.1007/978-3-662-08287-4_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08076-0
Online ISBN: 978-3-662-08287-4
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