An introduction to the geometry of numbers

Includes index

Includes bibliography (p. 334-343) and references.

Chapter I. Lattices 1. Introduction 2. Bases and sublattices 3. Lattices under linear transformation 4. Forms and lattices 5. The polar lattice

Chapter II. Reduction 1. Introduction 2. The basic process 3. Definite quadratic forms 4. Indefinite quadratic forms 5. Binary cubic forms 6. Other forms

Chapter III. Theorems of Blichfeldt and Minkowski 1. Introduction 2. Blichfeldt's and Mnowski's 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

Chapter IV. Distance functions 1. Introduction 2. General distance-functions 3. Convex sets 4. Distance functions and lattices

Chapter V. Mahler's 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. Speres 10. Applications to diophantine approximation

Chapter VI. The theorem of Minkowski-Hlawka 1. Introduction 2. Sublattices of prime index 3. The Minkowski-Hlawka theorem 4. Schmidt's theorems 5. A conjecture of Rogers 6. Unbounded star-bodies

Chapter VII. The quotient space 1. Introduction 2. General properties 3. The sum theorem

Chapter VIII. Successive minima 1. Introduction 2. Spheres 3. General distance-functions

Chapter IX. Packings 1. Introduction 2. Sets with V(/varphi) =n^2/Delta(/varphi) 3. Voronoi's results 4. Preparatory lemmas 5. Fejes Tóth's theorem 6. Cylinders 7. Packing of spheres 8. The proudctio of n linear forms

Chapter 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

Chapter XI. Ihomogeneous problems 1. Introduction 2. Convex sets 3. Transference theorems for convex sets 4. The producti of n linear forms

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 Monthly