The Use of Sections in the Theory of Perfect Quadratic Forms |
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³½ assume automorphs BARNES A 242 Chapter Corollary 2.2 correspond count the number COXETER defined definite quadratic form DETERMINANT NAME SYMBOL dimensional equivalent extreme forms face form associated form f Hence i₁ identity matrix implies integral lattice integral vector lattice packings lattice the sublattice Lemma Let f(x Math matrix minimal vectors minimum 2t2 mod 2t module neighbor number of minimal number of representations obtain p-face perfect forms PERFECT QUADRATIC FORMS perfect sections Pixi positive definite form positive definite quadratic reciprocal lattice representations of d(x restrict our attention SCOTT L=1 SCOTT SHIPP section of f sections of type senary SHIPP 68 SHIPP 97 SHIPP L=1 SHIPP SCOTT SHIPP SHIPP t₁ tế Theorem 2.5 theorem of Voronoi ù½ unimodular matrix unimodular transformation variables y₁ ỷ½ zero Σ Σ ΣΧ