Algebraic Number Theory
and over 360,000 other books are available for Amazon Kindle – Amazon’s new wireless reading device.
Learn more
| |||||||||||||||
Frequently Bought Together
Customers Who Bought This Item Also Bought
by Serge A. Lang
|
Commutative Algebra: with a View Toward Algebraic Geometry (Graduate Texts in Mathematics) by David Eisenbud |
by Jean Pierre Serre
|
by Robin Hartshorne
|
The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) by Joseph H. Silverman |
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
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
› Visit Amazon's Serge A. Lang Page
› Visit Amazon's Serge A. Lang Page
Inside This Book
(learn more)
First Sentence:
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 rational numbers Q). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
residue class field extension, admissible cycle, generalized ideal classes, modulo roots, ramification theorem, residue class degree, idele classes, multiplicative translation, class field theory, fractional ideal, archimedean absolute values, log mapping, finite separable extension, norm index, integral closure, ramified primes, decomposition group, restricted direct products, cyclotomic extensions, abelian extension, ideal class group, discrete valuation ring, multiplicative subset, ramification index, ramified extensions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hilbert's Theorem, Reine Angew New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
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 rational numbers Q). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
residue class field extension, admissible cycle, generalized ideal classes, modulo roots, ramification theorem, residue class degree, idele classes, multiplicative translation, class field theory, fractional ideal, archimedean absolute values, log mapping, finite separable extension, norm index, integral closure, ramified primes, decomposition group, restricted direct products, cyclotomic extensions, abelian extension, ideal class group, discrete valuation ring, multiplicative subset, ramification index, ramified extensions Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hilbert's Theorem, Reine Angew New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 34
books:
See all 34 books this book cites
100
books
cite this book:
See all 100 books citing this book
- Class Field Theory (Advanced Book Classics) by Emil Artin on 7 pages
- Basic Number Theory (Classics in Mathematics) by Andre Weil in Front Matter, page 177, and Back Matter
- Number Theory: An approach through history from Hammurapi to Legendre by André Weil on page 177, Back Matter (1), and Back Matter (2)
- Real and Functional Analysis (Graduate Texts in Mathematics) (v. 142) by Serge Lang in Front Matter, and Back Matter
- Algebraic Number Theory by H. Koch in Back Matter
See all 34 books this book cites
- Algebra by Serge Lang on 7 pages
- Problems in Algebraic Number Theory (Graduate Texts in Mathematics) by M. Ram Murty on 5 pages
- Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Graduate Texts in Mathematics) by Harold M. Edwards on 4 pages
- The Arithmetic of Hyperbolic 3-Manifolds by Colin Maclachlan on 4 pages
- One-Parameter Semigroups for Linear Evolution Equations (Graduate Texts in Mathematics) by Klaus-Jochen Engel in Back Matter (1), Back Matter (2), and Back Matter (3)
See all 100 books citing this book
Books on Related Topics
(learn more)
|
What Do Customers Ultimately Buy After Viewing This Item?
 |
84% buy the item featured on this page: Algebraic Number Theory (Graduate Texts in Mathematics) $62.95 |
 |
5% buy Algebra $51.58 |
 |
4% buy Algebraic Number Theory and Fermat's Last Theorem $59.00 |
 |
4% buy Elementary Number Theory $26.01 |
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Customer Reviews
|
Share your thoughts with other customers:
|
||||||||||||||||||||||
Most Helpful Customer Reviews
Share your thoughts with other customers: Create your own review
|
 |
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Listmania!
So You'd Like to...
|
|
Product Information from the Amapedia Community
Beta (What's this?)Be the first person to add an article about this item at Amapedia.com.
› See featured Amapedia.com articles
Look for Similar Items by Category
Look for Similar Items by Subject
Your Recent History
(What's this?)|
After viewing product detail pages or search results, look here to find an easy way to navigate back to pages you are interested in. |
