Algebraic Number Theory: 110 - Rilegato

Lang, Serge

Rilegato

ISBN 10: 0387942254 ISBN 13: 9780387942254

Casa editrice: Springer-Verlag New York Inc., 1994

Riassunto

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).

Su questo libro

Recensione

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

Contenuti

One General Basic Theory.- I Algebraic Integers.- II Completions.- III The Different and Discriminant.- IV Cyclotomic Fields.- V Parallelotopes.- VI The Ideal Function.- VII Ideles and Adeles.- VIII Elementary Properties of the Zeta Function and L-series.- Two Class Field Theory.- IX Norm Index Computations.- X The Artin Symbol, Reciprocity Law, and Class Field Theory.- XI The Existence Theorem and Local Class Field Theory.- XII L-series Again.- Three Analytic Theory.- XIII Functional Equation of the Zeta Function, Hecke’s Proof.- XIV Functional Equation, Tate’s Thesis.- XV Density of Primes and Tauberian Theorem.- XVI The Brauer-Siegel Theorem.- XVII Explicit Formulas.

Dettagli dell'edizione

• Editore: Springer-Verlag New York Inc.
• Data di pubblicazione: 1994
• Lingua: Inglese
• ISBN 10: 0387942254
• ISBN 13: 9780387942254
• Rilegatura: Copertina rigida
• Numero edizione: 2
• Numero di pagine: 370
• Contatto del produttore: non disponibile
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