This book is a revised and greatly expanded version of our book Elements of Number Theory published in 1972.As with the first book the primary audience we envisage consists of upper level underfraduate mathematics majors and graduate students.We have assumed some familiarity with the material in a standard undergraduate course in abstract algebra.

此书为英文版。

Preface to the Second Edition

Preface

CHAPTER 1 Unique Factorization

CHAPTER 2 Applications of Unique Factorization

CHAPTER 3 Congruence

CHAPTER 4　The Structure of U Z/nZ

CHAPTER 5　Quadratic Reciprocity

CHAPTER 6　Quadratic Gauss Sums

CHAPTER 7　Finite Fields

CHAPTER 8　Gauss and Jacobi Sums

CHAPTER 9　Cubic and Biquadratic Reciprocity

CHAPTER 10　Equations over Finite Fields

CHAPTER 11　The Zeta Function

CHAPTER 12　Algebraic Number Theory

CHAPTER 13　Quadratic and Cyclotomic Fields

CHAPTER 14　The Stickelberger Relation and the Eisenstein Reciprocity Law　

CHAPTER 15　Bernoulli Numbers

CHAPTER 16　Dirichlet L-functions

CHAPTER 17　Diophantine Equations

CHAPTER 18　Elliptic Curves

CHAPTER 19　The Mordeli-Weil Theorem　

CHAPTER 20　New Progress in Arithmetic Geometry

Select Hints for Exercise

Bibliography

Index