An Introduction to the Geometry of Numbers

Preface
Contents
Notation
Prologue
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 MINKOWSKI\'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. Spheres
	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
	4. Convex sets
	5. Polar convex bodies
Chapter IX. Packings
	1. Introduction
	2. Sets with V(S) = 2^n ⊿(S)
	3. VORONOï\'s results
	4. Preparatory lemmas
	5. FEJES TÓTH\'s theorem
	6. Cylinders
	7. Packing of spheres
	8. The product 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. Inhomogeneous problems
	1. Introduction
	2. Convex sets
	3. Transference theorems for convex sets
	4. Product of n linear forms
Appendix
References
Index