罗森编著的《函数域中的数论》内容介绍：基本数论和整数环的算术性质有关，在早期数论的发展过程中，学者已经注意到整数环和有限域上的多项式环之间的很多共同性质，例如，fermat和euler定理、wilson定理、二次（更高）互反性、素数定理以及算术级数中素数上的dirichlet定理，他们都存在着极大的相似性。本书在介绍完函数域上的基本资料以后，接下来深入剖析全局函数域和代数数域之间的相似性。内容丰富，包括abc-猜想、素数原根的artin猜想、brumer-stark猜想，drinfeld模型，类数公式和平均值定理。本书的前几章高年级本科生也可以理解，后面的章节更适合于研究生和数学专业以及相关专业的专家学者，增加了许多研究代数数域和代数函数域之间的关系的内容，本书也可以作为深入学习的基础教程。

Preface

1 Polynomials over Finite Fields

Exercises

2 Primes, Arithmetic Functions, and the Zeta Function

Exercises

3 The Reciprocity Law

Exercises

4 Dirichlet L-Series and Primes in an Arithmetic Progression

Exercises

5 Algebraic Function Fields and Global Function Fields

Exercises

6 Weil Differentials and the Canonical Class

Exercises

7 Extensions of Function Fields, Riemann-Hurwitz,and the ABC Theorem

Exercises

8 Constant Field Extensions

Exercises

9 Galois Extensions - Hecke and Artin L-Series

Exercises

10 Artin's Primitive Root Conjecture

Exercises

11 The Behavior of the Class Group in Constant Field Extensions

Exercises

12 Cyclotomic Function Fields

Exercises

13 Drinfeld Modules: An Introduction

Exercises

14 S-Units, S-Class Group, and the Corresponding L-Functions

Exercises

15 The Brumer-Stark Conjecture

Exercises

16 The Class Number Formulas in Quadratic

and Cyclotomic Function Fields

Exercises

17 Average Value Theorems in Function Fields

Exercises

Appendix: A Proof of the Function Field Riemann Hypothesis

Bibliography

Author Index

Subject Index