Author | Cassels, J. W. S. author |
---|---|
Title | An Introduction to the Geometry of Numbers [electronic resource] / by J. W. S. Cassels |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1997 |
Connect to | http://dx.doi.org/10.1007/978-3-642-62035-5 |
Descript | VIII, 345 p. online resource |
Prologue -- 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. BLICHFELDTโS and MINKOWSKIโS 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. MAHLERโS 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. SCHMIDTโS 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 V(L) = 2n?(L) -- 3. VORONOIโS results -- 4. Preparatory lemmas -- 5. FEJES TรThโS theorem -- 6. Cylinders -- 7. Packing of spheres -- 8. The product of n linear forms -- X. Automorphs -- 1. Introduction -- 2. Special forms -- 3. A method of MORDELL -- 4. Existence of automorphs -- 5. Isolation theorems -- 6. Applications of isolation -- 7. An infinity of solutions -- 8. Local methods -- XI. Inhomogeneous problems -- 1. Introduction -- 2. Convex sets -- 3. Transference theorems for convex sets -- 4. The product of n linear forms -- References