| Acknowledgemetns | 第1-8页 |
| 摘要 | 第8-9页 |
| Abstract | 第9-11页 |
| Preface | 第11-12页 |
| Chapter 1 Introduction | 第12-23页 |
| ·Explicit class field theory | 第13-18页 |
| ·Our approach to Real Multiplication | 第18页 |
| ·Noncommutative geometry, Manin's approach | 第18-23页 |
| Chapter 2 Formal moduli space of real quadratic tori with Real Mul-tiplication | 第23-29页 |
| ·Real quadratic tori with Real Multiplication | 第23-25页 |
| ·formal moduli space of real quadratic tori with RM and formal modular forms | 第25-29页 |
| Chapter 3 Formal Eisenstein series their applications to real multi-plication | 第29-33页 |
| ·The q-expansion of formal Eisenstein series | 第29-31页 |
| ·An application to real multiplication | 第31-33页 |
| Chapter 4 A conjecture on the geometric structure of the formal moduli space Q | 第33-38页 |
| ·Correspondence between real quadratic formal moduli space Q and set of prime closed geodesies on upper half plane | 第33-34页 |
| ·An evidence of Real multiplication | 第34-36页 |
| ·Prime geodesic theorem and our conjecture | 第36-38页 |
| Chapter 5 A independent result | 第38-46页 |
| ·Introduction | 第38页 |
| ·An expression for primes p≡1(mod 8) | 第38-46页 |
| REFERENCES | 第46-49页 |
