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Graduate Texts in Mathematics

Algebraic Number Theory

Authors: Lang, Serge

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About this Textbook

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 I 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 Weber, 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, I have intermingled the ideal and idelic approaches without prejudice for either. I 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).

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


Table of contents (17 chapters)

Table of contents (17 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-1-4684-0296-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Number Theory
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
110
Copyright
1986
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4684-0296-4
DOI
10.1007/978-1-4684-0296-4
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XIII, 354
Number of Illustrations
1 b/w illustrations
Additional Information
Originally published by Addison-Wesley Publishing Company, 1970
Topics