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Algebraic Number Theory : Graduate Texts in Mathematics - Serge Lang

Algebraic Number Theory

Graduate Texts in Mathematics

Hardcover

Published: 24th June 1994
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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. 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. This new edition contains corrections, as well as several additions to the previous edition, and the last chapter on explicit formulas has been rewritten.

Second Edition

S. Lang

Algebraic Number Theory

"This book is the second edition of Lang's famous and indispensable book on algebraic number theory. The major change from the previous edition is that the last chapter on explicit formulas has been completely rewritten. In addition, a few new sections have been added to the other chapters . . . 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

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
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387942254
ISBN-10: 0387942254
Series: Graduate Texts in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 357
Published: 24th June 1994
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.3 x 16.4  x 2.7
Weight (kg): 0.74
Edition Number: 2
Edition Type: Revised