## The Use of Sections in the Theory of Perfect Quadratic Forms |

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### Contents

Development of Basic Theorems | 12 |

Sections of A and Atqr | 28 |

Sections of Bt and Btqr | 39 |

3 other sections not shown

### Common terms and phrases

apply the transformation assume automorphs BARNES A 242 Chapter Corollary 2.2 COXETER defined definite quadratic form det(f det(g DETERMINANT NAME SYMBOL equivalent extreme forms families of forms form associated form f form f(x forms in dimensions ft given Hence identity matrix implies integral lattice integral vector L-l A-l L«l A«l lattice packings lattice the sublattice Lemma Let f(x linear forms Math minimum 2t minimum of d(x mod 2t multiple neighbor number of minimal number of representations obtain p-face PERFECT QUADRATIC FORMS perfect sections positive definite form positive definite quadratic reciprocal lattice representations of d(x restrict our attention satisfy p'x section of f sections of type senary shape SHIPP L=l A=l sublattice of ft supremum Theorem 2.5 theorem of Voronoi thesis unimodular matrix unimodular transformation University of Wisconsin vectors of f zero