| Chinese Abstract | 第4-5页 |
| Abstract | 第5页 |
| Chapter 1 Representation by positive definite integral quadratic forms | 第9-15页 |
| 1.1 Basic notions and Problems | 第9-11页 |
| 1.2 Modular forms and the Eichler Commutation Relation | 第11-12页 |
| 1.3 The Cooper and Lam's Conjecture | 第12-13页 |
| 1.4 Representation by ternary quadratic forms | 第13-15页 |
| Chapter 2 Eichler's commutation relation and some other invariant subspaces of Hecke operators | 第15-43页 |
| 2.1 Introduction | 第15-18页 |
| 2.2 Theta functions | 第18-21页 |
| 2.3 Some lemmas | 第21-24页 |
| 2.4 Main results | 第24-38页 |
| 2.5 Eisenstein Series and cusp forms | 第38-41页 |
| 2.6 An example for ternary quadratic forms on anisotropic spaces | 第41-43页 |
| Chapter 3 Multiplicative property of representation numbers of ternary quadratic forms | 第43-55页 |
| 3.1 Introduction | 第43-48页 |
| 3.2 Invariant subspace | 第48-50页 |
| 3.3 The coefficients of the theta function of the genus | 第50-51页 |
| 3.4 The coefficients of the theta function of L | 第51-53页 |
| 3.5 Cooper and Lam's conjecture | 第53-55页 |
| Chapter 4 Eligible integers represented by positive ternary quadratic forms | 第55-62页 |
| 4.1 Introduction | 第55-57页 |
| 4.2 Proof of Theorem 4.1.3 | 第57-60页 |
| 4.3 Applications | 第60-62页 |
| REFERENCES | 第62-65页 |
| Published and unpublished papers | 第65-66页 |
| Acknowledgements | 第66-67页 |
