Algebraic Number Theory (Addison-Wesley Series in Mathematics) - Hardcover

Serge A. Lang

Hardcover

ISBN 10: 0201042010 ISBN 13: 9780201042016

Publisher: Addison Wesley Publishing Company, 1970

Synopsis

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 theorem, and Weil's explicit formulas. This new 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

Review

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

Edition details

• Publisher: Addison Wesley Publishing Company
• Publication date: 1970
• Language: English
• ISBN 10: 0201042010
• ISBN 13: 9780201042016
• Binding: Hardcover
• Number of pages: 354