Lecture Notes on Geometry of Numbers

1. Preliminaries.- 2. Minkowski's Fundamental Theorem and its Applications.- 3. Lattices.- 4. Minima of Positive De nite Quadratic Forms.- 5. Critical Determinant.- 6. Successive Minima.- 7. Packings Density.- 8. Coverings.- 9. Homogeneous Minimum.- 10. Inhomogeneous Problems.

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• Teoria dos números
• Geometria algébrica

lattices;convex sets;Minkowski fundamental theorem;critical determinants;Minkowski second inequality;packing;coverings density;covering constant;quadratic forms;homogeneous minima;non-homogeneous minima;Watson's conjecture;Minkowski's conjecture