Arithmetic of Quadratic Forms Book

	Preface
	Notation
Ch. 1	General theory of quadratic forms	1
1.1	Symmetric bilinear forms	1
1.2	Quadratic forms	3
1.3	Quadratic forms over finite fields	12
1.4	The Clifford algebra	20
1.5	Quaternion algebras	24
1.6	The spinor norm	29
1.7	Scalar extensions	32
Ch. 2	Positive definite quadratic forms over R	33
2.1	Reduction theory	33
2.2	An estimate of Hermite's constant	42
Ch. 3	Quadratic forms over local fields	47
3.1	p-adic numbers	47
3.2	The quadratic residue symbol	52
3.3	The Hilbert symbol	54
3.4	The Hasse Invariant	56
3.5	Classification of quadratic spaces over p-adic number fields	60
Ch. 4	Quadratic forms over Q	64
Ch. 5	Quadratic forms over the p-adic integer ring	70
5.1	Dual lattices	70
5.2	Maximal and modular lattices	71
5.3	Jordan decompositions	79
5.4	Extension theorems	86
5.5	The spinor norm	92
5.6	Local densities	93
Ch. 6	Quadratic forms over Z	129
6.1	Fundamentals	129
6.2	Approximation theorems	134
6.3	Genus, spinor genus and class	147
6.4	Representation of codimension 1	151
6.5	Representation of codimension 2	157
6.6	Representation of codimension [actual symbol not reproducible] 3	164
6.7	Orthogonal decomposition	169
6.8	The Minkowski-Siegel formula	173
Ch. 7	Some functorial properties of positive definite quadratic forms	189
7.1	Positive lattices of type	190
7.2	A fundamental lemma	199
7.3	Weighted graphs	217
7.4	The tensor product of positive lattices	222
7.5	Scalar extension of positive lattices	239
	Notes	240
	References	263
	Index	268