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Number Theory 2: Introduction to Class Field Theory

Kazuya Kato University of Chicago, Chicago, IL
Nobushige Kurokawa Tokyo Institute of Technology, Tokyo, Japan
Takeshi Saito University of Tokyo, Tokyo, Japan
Available Formats:
Softcover ISBN: 978-0-8218-1355-3
Product Code: MMONO/240
List Price: $52.00 MAA Member Price:$46.80
AMS Member Price: $41.60 Electronic ISBN: 978-1-4704-1815-1 Product Code: MMONO/240.E List Price:$52.00
MAA Member Price: $46.80 AMS Member Price:$41.60
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List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $62.40 Click above image for expanded view Number Theory 2: Introduction to Class Field Theory Kazuya Kato University of Chicago, Chicago, IL Nobushige Kurokawa Tokyo Institute of Technology, Tokyo, Japan Takeshi Saito University of Tokyo, Tokyo, Japan Available Formats:  Softcover ISBN: 978-0-8218-1355-3 Product Code: MMONO/240  List Price:$52.00 MAA Member Price: $46.80 AMS Member Price:$41.60
 Electronic ISBN: 978-1-4704-1815-1 Product Code: MMONO/240.E
 List Price: $52.00 MAA Member Price:$46.80 AMS Member Price: $41.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$62.40
• Book Details

Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics
Volume: 2402011; 240 pp
MSC: 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 local-global 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)

• Reviews

• The authors' presentation is very reader-friendly. ...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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Iwanami Series in Modern Mathematics
Volume: 2402011; 240 pp
MSC: 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 local-global 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 reader-friendly. ...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
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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