| 摘要 | 第1-7页 |
| Abstract | 第7-10页 |
| Chapter 1 Algebraic function fields and their extension fields | 第10-35页 |
| ·Riemann-Roch theorem and Riemman-Hurwitz formula | 第10-14页 |
| ·Zeta function of global function fields | 第14-22页 |
| ·Algebraic function fields of the form K(?) | 第22-35页 |
| Chapter 2 Genus theory and the structure of class groups of global function fields | 第35-49页 |
| ·Genus theory and Conner-Hurrelbrink exact hexagon for global function fields | 第35-40页 |
| ·l-class group of cyclic extensions of prime degree l of global function fields | 第40-49页 |
| Chapter 3 Drinfeld module theory and cyclotomic function fields | 第49-73页 |
| ·Introduction to Drinfeld module theory | 第49-58页 |
| ·Carlitz module and cyclotomic function fields | 第58-65页 |
| ·Analytic class number formulas for subfields of some cyclotomic function fields | 第65-73页 |
| Chapter 4 On the reducibility of binary affine polynomials | 第73-83页 |
| ·Introduction to background | 第73-75页 |
| ·Some known results about polynomials over finite fields | 第75-78页 |
| ·The reducibility of affine pentanomials over F_2 | 第78-83页 |
| REFERENCES | 第83-87页 |
| Papers completed during my PhD program | 第87-88页 |
| 个人简历 | 第88-89页 |
| 致谢 | 第89-90页 |
