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Lecture XII

In: Lectures on the Geometry of Numbers

Author

Listed:
  • Carl Ludwig Siegel
  • Komaravolu Chandrasekharan

    (ETH Zürich, Mathematik)

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 $${r_2}\left( {{x^2} + xy + {y^2}} \right)$$ .

Suggested Citation

  • Carl Ludwig Siegel & Komaravolu Chandrasekharan, 1989. "Lecture XII," Springer Books, in: Lectures on the Geometry of Numbers, pages 118-126, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-08287-4_12
    DOI: 10.1007/978-3-662-08287-4_12
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