Lecture XII

Carl Ludwig Siegel and Komaravolu Chandrasekharan
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Komaravolu Chandrasekharan: ETH Zürich, Mathematik

A chapter in Lectures on the Geometry of Numbers, 1989, pp 118-126 from Springer

Abstract: 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 ${r_2} \leqslant \sqrt {\frac{{4\Delta }}{3}} ,$ 1 $${r_2} \leqslant \sqrt {\frac{{4\Delta }}{3}} ,$$ and the equality sign holds if and only if the form is equivalent to 2 $${r_2}\left( {{x^2} + xy + {y^2}} \right)$$ .

Date: 1989
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DOI: 10.1007/978-3-662-08287-4_12

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