Algebraic Number Theory

ISBN-10: 0387942254

ISBN-13: 9780387942254

Edition: 2nd 1994 (Revised)

Authors: Serge A. Lang

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Description:

This is a corrected printing of the 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. Part I introduces some of the basic ideas of the theory: number fields, ideal classes, ideles and adeles, and zeta functions. It also contains a version of a Riemann-Roch theorem in number fields, proved by Lang in the very first version of the book in the sixties. This version can now be seen as a precursor of Arakelov theory. Part II covers class field theory, and Part III is devoted to analytic methods, including an exposition of Tate's thesis, the Brauer-Siegel theorem, and Weil's explicit formulas. The second edition contains corrections, as well as several additions to the previous edition, and the last chapter on explicit formulas has been rewritten.
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Book details

List price: $79.99
Edition: 2nd
Copyright year: 1994
Publisher: Springer
Publication date: 7/19/2000
Binding: Hardcover
Pages: 357
Size: 6.50" wide x 9.50" long x 1.00" tall
Weight: 1.540
Language: English

Lang, Yale University, New Haven, CT.

Algebraic Integers
Completions
The Different and Discriminant
Cyclotomic Fields
Parallelotopes
The Ideal Function
Ideles and Adeles
Elementary Properties of the Zeta Function and L-series
Norm Index Computations
The Artin Symbol, Reciprocity Law, and Class Field Theory
The Existence Theorem and Local Class Field Theory
L-series Again
Functional Equation of the Zeta Function, Hecke's Proof
Functional Equation, Tate's Thesis
Density of Primes and Tauberian Theorem
The Brauer-Siegel Theorem
Explicit Formulas
Bibliography
Index
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