出版时间:2003-6 出版社:世界图书出版公司 作者:Kenneth. Ireland 页数:389
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内容概要
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.
书籍目录
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/nZCHAPTER 5 Quadratic ReciprocityCHAPTER 6 Quadratic Gauss SumsCHAPTER 7 Finite FieldsCHAPTER 8 Gauss and Jacobi SumsCHAPTER 9 Cubic and Biquadratic ReciprocityCHAPTER 10 Equations over Finite FieldsCHAPTER 11 The Zeta FunctionCHAPTER 12 Algebraic Number TheoryCHAPTER 13 Quadratic and Cyclotomic FieldsCHAPTER 14 The Stickelberger Relation and the Eisenstein Reciprocity Law CHAPTER 15 Bernoulli NumbersCHAPTER 16 Dirichlet L-functionsCHAPTER 17 Diophantine EquationsCHAPTER 18 Elliptic CurvesCHAPTER 19 The Mordeli-Weil Theorem CHAPTER 20 New Progress in Arithmetic GeometrySelect Hints for ExerciseBibliographyIndex
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