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Algebraic Number Theory

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This is a second edition of Lang's well-known textbook. It covers all of the basic material of classical algebraic number theory, giving the student the background necessary for the study of further topics in algebraic number theory, such as cyclotomic fields, or modular forms.

"Lang's books are always of great value for the graduate student and the research mathematician. This updated edition of Algebraic number theory is no exception."―-MATHEMATICAL REVIEWS

Author(s): Serge Lang
Series: Graduate Texts in Mathematics 110
Edition: 2nd
Publisher: Springer
Year: 1994

Language: English
Pages: 357

Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Algebraic Integers....Pages 3-30
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 155-172
Front Matter....Pages 173-178
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 331-351
Back Matter....Pages 353-357