Preface
Part Ⅰ--Algebraic Methods
Chapter Ⅰ--Finite fields
1--Generalities
2--Equations over a finite field
3--Quadratic reciprocity law
Appendix--Another proof of the quadratic reciprocity law
Chapter Ⅱ--p-adic fields
1--The ring Zp and the field Qp
2--p-adic equations
3--The multiplicative group of Qp
Chapter Ⅲ--Hilbert symbol
1--Local properties
2--Global properties
ChapterⅣ--Quadratic forms over Qp and over Q
I--Quadratic forms
2--Quadratic forms over Qp
3--Quadratic forms over Q
Appendix--Sums of three squares
Chapter Ⅴ--Integral quadratic forms with discriminant ± 1
l--Preliminaries
2--Statement of results
3--Proofs
Part Ⅱ--Analytic Methods
Chapter Ⅵ--The theorem on arithmetic progressions
I--Characters of finite abelian groups
2--Dirichlet series
3--Zeta function and L functions
4---Density and Dirichlet theorem
Chapter Ⅶ--Modular forms
1--The modular group
2--Modular functions
3--The space of modular forms
4--Expansions at infinity
5--Hecke operators
6--Theta functions
