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Algebraic Number Theory : Applied Mathematical Sciences (Springer) - Serge Lang

Algebraic Number Theory

Applied Mathematical Sciences (Springer)

Hardcover Published: 19th July 2000
ISBN: 9780387942254
Number Of Pages: 357

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The present book gives an exposition of the classical basic algebraic and analytic number theory and supersedes my Algebraic Numbers, including much more material, e. g. the class field theory on which 1 make further comments at the appropriate place later. For different points of view, the reader is encouraged to read the collec- tion of papers from the Brighton Symposium (edited by Cassels-Frohlich), the Artin-Tate notes on class field theory, Weil's book on Basic Number Theory, Borevich-Shafarevich's Number Theory, and also older books like those of W eber, Hasse, Hecke, and Hilbert's Zahlbericht. It seems that over the years, everything that has been done has proved useful, theo- retically or as examples, for the further development of the theory. Old, and seemingly isolated special cases have continuously acquired renewed significance, often after half a century or more. The point of view taken here is principally global, and we deal with local fields only incidentally. For a more complete treatment of these, cf. Serre's book Corps Locaux. There is much to be said for a direct global approach to number fields. Stylistically, 1 have intermingled the ideal and idelic approaches without prejudice for either. 1 also include two proofs of the functional equation for the zeta function, to acquaint the reader with different techniques (in some sense equivalent, but in another sense, suggestive of very different moods).

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

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: Applied Mathematical Sciences (Springer)
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 357
Published: 19th July 2000
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 24.03 x 16.31  x 2.49
Weight (kg): 0.64
Edition Number: 2
Edition Type: Revised

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