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Algebraic Number Theory (Graduate Texts in Mathematics) (Hardcover)

~ Serge Lang (Author) "This chapter describes the basic aspects of the ring of algebraic integers in a number field (always assumed to be of finite degree over the..." (more)
Key Phrases: residue class field extension, admissible cycle, generalized ideal classes, Hilbert's Theorem, Reine Angew (more...)
5.0 out of 5 stars  See all reviews (1 customer review)

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Editorial Reviews

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


Product Description

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.

Product Details

  • Hardcover: 357 pages
  • Publisher: Springer; 2nd edition (July 19, 2000)
  • Language: English
  • ISBN-10: 0387942254
  • ISBN-13: 978-0387942254
  • Product Dimensions: 9.1 x 6.4 x 1.1 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon.com Sales Rank: #548,354 in Books (See Bestsellers in Books)

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Serge A. Lang
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2 of 3 people found the following review helpful:
5.0 out of 5 stars Classic, April 17, 2009
Awesome text. For the more well-versed reader in Algebraic Number Theory. Great resource for a variety of topics.
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