Algebraic Number Theory (Graduate Texts in Mathematics) - Hardcover

Serge Lang

Hardcover

ISBN 10: 3540942254 ISBN 13: 9783540942252

Publisher: Springer Verlag, Secaucus, New Jersey, U.S.A., 1994

Synopsis

This is a corrected printing of the 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 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. The second edition contains corrections, as well as several additions to the previous edition, and the last chapter on explicit formulas has been rewritten.

About this title

From the Back Cover

From the reviews of the first printing, published as Volume 62 of the Encyclopaedia of Mathematical Sciences:

"... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes."
Monatshefte fuer Mathematik, 1994
"... Koch's book is written mostly for non-specialists. It is an up-to-date account of the subject dealing with mostly general questions. Special results appear only as illustrating examples for the general features of the theory. It is supposed that the reader has good general background in the fields of modern (abstract) algebra and elementary number theory. We recommend this volume mainly to graduate studens and research mathematicians."
Acta Scientiarum Mathematicarum, 1993

Review

From the reviews: "... The author succeeded in an excellent way to describe the various points of view under which Class Field Theory can be seen. ... In any case the author succeeded to write a very readable book on these difficult themes." Monatshefte fuer Mathematik, 1994 "... Number theory is not easy and quite technical at several places, as the author is able to show in his technically good exposition. The amount of difficult material well exposed gives a survey of quite a lot of good solid classical number theory... Conclusion: for people not already familiar with this field this book is not so easy to read, but for the specialist in number theory this is a useful description of (classical) algebraic number theory." Medelingen van het wiskundig genootschap, 1995

Edition details

• Publisher: Springer Verlag, Secaucus, New Jersey, U.S.A.
• Publication date: 1994
• Language: English
• ISBN 10: 3540942254
• ISBN 13: 9783540942252
• Binding: Hardcover
• Edition number: 2