## An Introduction to the Geometry of NumbersFrom the reviews: "The work is carefully written. It is well motivated, and interesting to read, even if it is not always easy... historical material is included... the author has written excellent account of an interesting subject." Mathematical Gazette "A well-written, very thorough account ... Among the topi are lattices, reduction, Minkowskis Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references." The American Mathematical Monthly |

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### Contents

II | 1 |

III | 9 |

IV | 19 |

V | 20 |

VI | 23 |

VII | 26 |

VIII | 27 |

IX | 30 |

XXXVII | 184 |

XXXVIII | 187 |

XXXIX | 189 |

XL | 194 |

XLI | 198 |

XLII | 201 |

XLIII | 205 |

XLIV | 207 |

X | 35 |

XI | 51 |

XII | 60 |

XIII | 64 |

XIV | 68 |

XV | 73 |

XVI | 78 |

XVII | 80 |

XVIII | 84 |

XIX | 98 |

XX | 103 |

XXI | 105 |

XXII | 108 |

XXIII | 119 |

XXIV | 121 |

XXV | 122 |

XXVI | 126 |

XXVII | 134 |

XXVIII | 141 |

XXIX | 145 |

XXX | 152 |

XXXI | 155 |

XXXII | 163 |

XXXIII | 165 |

XXXIV | 175 |

XXXV | 178 |

XXXVI | 181 |

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### Common terms and phrases

2-dimensional admissible lattices arbitrarily small automorph boundary point bounded bounded set Cassels Chapter clearly co-ordinates coefficients concludes the proof continued fractions contradiction convex body theorem convex set convex symmetric Corollary critical lattice Davenport defined definite quadratic form denote determinant distance function distance-function equivalent euclidean space example exist finite number follows at once further Geometry of Numbers given Hence homogeneous linear transformation hyperplane inequality infimum infinitely integers lattice constant Lemma Let F(x linear forms linearly independent points Mahler Minkowski-Hlawka Theorem Minkowski's convex body Minkowski's theorem Mordell non-singular obtain packing parallelogram parallelopiped points x1 positive number proof of Theorem properties proportional to integral quotient space real numbers result right-hand side Rogers satisfies sequence set f set of points shape sphere star-body successive minima suppose without loss symmetric convex tac-plane Theorem II Theorem VII trivial values vectors VIII volume