Algebraic Number Theory

Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Algebraic Integers....Pages 3-29
Completions....Pages 31-55
The Different and Discriminant....Pages 57-69
Cyclotomic Fields....Pages 71-98
Parallelotopes....Pages 99-122
The Ideal Function....Pages 123-135
Ideles and Adeles....Pages 137-154
Elementary Properties of the Zeta Function and L -series....Pages 155-170
Front Matter....Pages 171-177
Norm Index Computations....Pages 179-195
The Artin Symbol, Reciprocity Law, and Class Field Theory....Pages 197-212
The Existence Theorem and Local Class Field Theory....Pages 213-227
 L -Series Again....Pages 229-239
Front Matter....Pages 241-243
Functional Equation of the Zeta Function, Hecke’s Proof....Pages 245-273
Functional Equation, Tate’s Thesis....Pages 275-301
Density of Primes and Tauberian Theorem....Pages 303-319
The Brauer-Siegel Theorem....Pages 321-330
Explicit Formulas....Pages 331-349
Back Matter....Pages 351-354