## 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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### Table des matières

9 | |

Reduction | 26 |

Representation of integers by quadratic forms | 99 |

MAHLERs compactness theorem | 121 |

The theorem of MINKowskiHLAwKA | 175 |

The quotient space | 194 |

Successive minima | 201 |

Packings | 223 |

Automorphs | 256 |

Inhomogeneous problems | 303 |

Appendix | 332 |

Index | 343 |

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### Expressions et termes fréquents

9°-admissible admissible lattice arbitrarily small automorph boundary of 9 boundary point bounded bounded set Cassels Chapter clearly co-ordinates coefficients concludes the proof continued fractions convex body theorem convex set convex symmetric Corollary critical lattice DAVENPORT defined definite quadratic form denote diophantine approximation distance function equivalent exist finite number follows at once geometry of numbers given Hence homogeneous linear transformation hyperplane inequality infimum infinitely integers lattice constant Lemma Let b1 Let F(a linear forms linearly independent points Lond MAHLER Math Minkowski-Hlawka Theorem MINKowski's convex body MINKowski's theorem MORDELL n-dimensional non-singular packing parallelogram parallelopiped point of 9 points a1 positive number proof of Theorem properties proportional to integral quotient space real numbers result ROGERS satisfies sequence set 9 set of points shape sphere star-body successive minima suppose without loss symmetric convex tac-plane Theorem IV Theorem VII trivial values vectors VIII volume