TABLE OF CONTENTS
Preface vii
Notation and Terminology ix
Introduction 1
Chapter I. Algebraic theory of quadratic forms, Clifford
algebras, and spin groups 9
1. Quadratic forms and associative algebras 9
2. Clifford algebras 15
3. Clifford groups and spin groups 20
4. Parabolic subgroups 28
Chapter II. Quadratic forms, Clifford algebras, and spin
groups over a local or global field 37
5. Orders and ideals in an algebra 37
6. Quadratic forms over a local field 45
7. Lower-dimensional cases and the Hasse principle 52
Part I. Clifford groups over a local field 62
Part II. Formal Hecke algebras and formal Euler factors 72
9. Orthogonal, Clifford, and spin groups over a global field 80
Chapter III. Quadratic Diophantine equations 93
10. Quadratic Diophantine equations over a local field 93
11. Quadratic Diophantine equations over a global field 101
12. The class number of an orthogonal group and sums of
squares 113
13. Nonscalar quadratic Diophantine equations; Connection
with the mass formula; A historical perspective 126
Chapter IV. Groups and symmetric spaces over R 139
14. Clifford and spin groups over R; The case of signature
(1, m) 139
15. The case of signature (2, m) 146
16. Orthogonal groups over R and symmetric spaces 154
Chapter V. Euler products and Eisenstein series on or-
thogonal groups 163
17. Automorphic forms and Euler products on an orthogonal
group 163
