描述
开 本: 16开纸 张: 胶版纸包 装: 平装-胶订是否套装: 否国际标准书号ISBN: 9787506260152
内容简介
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
目 录
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
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
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