Softcover ISBN:  9780821813553 
Product Code:  MMONO/240 
List Price:  $52.00 
MAA Member Price:  $46.80 
AMS Member Price:  $41.60 
Electronic ISBN:  9781470418151 
Product Code:  MMONO/240.E 
List Price:  $52.00 
MAA Member Price:  $46.80 
AMS Member Price:  $41.60 

Book DetailsTranslations of Mathematical MonographsIwanami Series in Modern MathematicsVolume: 240; 2011; 240 ppMSC: Primary 11;
This book, the second of three related volumes on number theory, is the English translation of the original Japanese book. Here, the idea of class field theory, a highlight in algebraic number theory, is first described with many concrete examples. A detailed account of proofs is thoroughly exposited in the final chapter. The authors also explain the localglobal method in number theory, including the use of ideles and adeles. Basic properties of zeta and \(L\)functions are established and used to prove the prime number theorem and the Dirichlet theorem on prime numbers in arithmetic progressions. With this book, the reader can enjoy the beauty of numbers and obtain fundamental knowledge of modern number theory.
The translation of the first volume was published as Number Theory 1: Fermat's Dream, Translations of Mathematical Monographs (Iwanami Series in Modern Mathematics), vol. 186, American Mathematical Society, 2000.ReadershipGraduate students and research mathematicians interested in number theory.

Table of Contents

Chapters

What is class field theory?

Local and global fields

$\zeta $ (II)

Class field theory (II)


Additional Material

Reviews

The authors' presentation is very readerfriendly. ...Their style of writing is lively and inspiring. ...The book can warmly be recommended to anyone interested in reading a modern exposition of class field theory.
Mathematical Reviews


RequestsReview Copy – for reviewers who would like to review an AMS bookDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
This book, the second of three related volumes on number theory, is the English translation of the original Japanese book. Here, the idea of class field theory, a highlight in algebraic number theory, is first described with many concrete examples. A detailed account of proofs is thoroughly exposited in the final chapter. The authors also explain the localglobal method in number theory, including the use of ideles and adeles. Basic properties of zeta and \(L\)functions are established and used to prove the prime number theorem and the Dirichlet theorem on prime numbers in arithmetic progressions. With this book, the reader can enjoy the beauty of numbers and obtain fundamental knowledge of modern number theory.
The translation of the first volume was published as Number Theory 1: Fermat's Dream, Translations of Mathematical Monographs (Iwanami Series in Modern Mathematics), vol. 186, American Mathematical Society, 2000.
Graduate students and research mathematicians interested in number theory.

Chapters

What is class field theory?

Local and global fields

$\zeta $ (II)

Class field theory (II)

The authors' presentation is very readerfriendly. ...Their style of writing is lively and inspiring. ...The book can warmly be recommended to anyone interested in reading a modern exposition of class field theory.
Mathematical Reviews