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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
Number Theory 2
Number Theory 2
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
eBook ISBN:  978-1-4704-1815-1
Product Code:  MMONO/240.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $39.20
Softcover ISBN:  978-0-8218-1355-3
eBook: ISBN:  978-1-4704-1815-1
Product Code:  MMONO/240.B
List Price: $101.00$76.50
MAA Member Price: $90.90$68.85
AMS Member Price: $80.80$61.20
Number Theory 2
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Number Theory 2
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
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
eBook ISBN:  978-1-4704-1815-1
Product Code:  MMONO/240.E
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $39.20
Softcover ISBN:  978-0-8218-1355-3
eBook ISBN:  978-1-4704-1815-1
Product Code:  MMONO/240.B
List Price: $101.00$76.50
MAA Member Price: $90.90$68.85
AMS Member Price: $80.80$61.20
  • 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.

    Readership

    Graduate 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)
  • 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 publishers of book reviews
    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.

Readership

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 publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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