Algebraic Number Theory

By: Serge Lang

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Hardcover | 1 August 2000 | Edition Number 2

At a Glance

Hardcover
376 Pages

Edition Type
Revised

Dimensions(cm)
24.13 x 16.51 x 2.54

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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

Industry Reviews

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

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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.

Algebraic Number Theory

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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