| Abstract in Chinese | 第4-5页 |
| Abstract in English | 第5页 |
| Chapter 1 Backgrounds and main theorems | 第6-11页 |
| §1.1 Preliminaries | 第6-8页 |
| §1.2 Introduction to the sumsets of weighted exceptional units and thediagonal quadratic forms | 第8-11页 |
| Chapter 2 On the sumsets of weighted exceptional units in a finite commu-tative ring | 第11-17页 |
| §2.1 Some important lemmas | 第11-14页 |
| §2.2 Proof of the main theorem | 第14页 |
| §2.3 A example on Galois rings | 第14-17页 |
| Chapter 3 The number of solutions of diagonal quadratic forms over Galoisrings GR(p~2,p~(2m)) | 第17-24页 |
| §3.1 Some important lemmas | 第17-19页 |
| §3.2 Proofs of the main theorems | 第19-24页 |
| Bibliography | 第24-27页 |
| 致谢 | 第27页 |
