An Introduction to the Geometry of Numbers [Paperback]

From 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 MonthlyPrologue.- I. Lattices.- 1. Introduction.- 2. Bases and sublattices.- 3. Lattices under linear transformation.- 4. Forms and lattices.- 5. The polar lattice.- II. Reduction.- 1. Introduction.- 2. The basic process.- 3. Definite quadratic forms.- 4. Indefinite quadratic forms.- 5. Binary cubic forms.- 6. Other forms.- III. Theorems of BLICHFELDT and MINKOWSKI.- 1. Introduction.- 2. BLICHFELDTS and MINKOWSKIS theorems.- 3. Generalisations to non-negative functions.- 4. Characterisation of lattices.- 5. Lattice constants.- 6. A method of MORDELL.- 7. Representation of integers by quadratic forms.- IV. Distance functions.- 1. Introduction.- 2. General distance-functions.- 3. Convex sets.- 4. Distance functions and lattices.- V. MAHLERS compactness theorem.- 1. Introduction.- 2. Linear transformations.- 3. Convergence of lattices.- 4. Compactness for lattices.- 5. Critical lattices.- 6. Bounded star-bodies.- 7. Reducibility.- 8. Convex bodies.- 9. Spheres.- 10. Applications to diophantine approximation.- VI. The theorem of MINKOWSKI-HLAWKA.- 1. Introduction.- 2. Sublattices of prime index.- 3. The Minkowski-Hlawka theorem.- 4. SCHMIDTS theorems.- 5. A conjecture of ROGERS W.- 6. Unbounded star-bodies.- VII. The quotient space.- 1. Introduction.- 2. General properties.- 3. The sum theorem.- VIII. Successive minima.- 1. Introduction.- 2. Spheres.- 3. General distance-functions.- 4. Convex sets.- 5. Polar convex bodies.- IX. Packings.- 1. Introduction.- 2. Sets with Vl3v