Ebook: A Classical Introduction to Modern Number Theory

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Content:
Front Matter....Pages i-xiii
Unique Factorization....Pages 1-16
Applications of Unique Factorization....Pages 17-27
Congruence....Pages 28-38
The Structure of U(?/n?)....Pages 39-49
Quadratic Reciprocity....Pages 50-65
Quadratic Gauss Sums....Pages 66-78
Finite Fields....Pages 79-87
Gauss and Jacobi Sums....Pages 88-107
Cubic and Biquadratic Reciprocity....Pages 108-137
Equations over Finite Fields....Pages 138-150
The Zeta Function....Pages 151-171
Algebraic Number Theory....Pages 172-187
Quadratic and Cyclotomic Fields....Pages 188-202
The Stickelberger Relation and the Eisenstein Reciprocity Law....Pages 203-227
Bernoulli Numbers....Pages 228-248
Dirichlet L-functions....Pages 249-268
Diophantine Equations....Pages 269-296
Elliptic Curves....Pages 297-318
Back Matter....Pages 319-344

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Content:
Front Matter....Pages i-xiii
Unique Factorization....Pages 1-16
Applications of Unique Factorization....Pages 17-27
Congruence....Pages 28-38
The Structure of U(?/n?)....Pages 39-49
Quadratic Reciprocity....Pages 50-65
Quadratic Gauss Sums....Pages 66-78
Finite Fields....Pages 79-87
Gauss and Jacobi Sums....Pages 88-107
Cubic and Biquadratic Reciprocity....Pages 108-137
Equations over Finite Fields....Pages 138-150
The Zeta Function....Pages 151-171
Algebraic Number Theory....Pages 172-187
Quadratic and Cyclotomic Fields....Pages 188-202
The Stickelberger Relation and the Eisenstein Reciprocity Law....Pages 203-227
Bernoulli Numbers....Pages 228-248
Dirichlet L-functions....Pages 249-268
Diophantine Equations....Pages 269-296
Elliptic Curves....Pages 297-318
Back Matter....Pages 319-344
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