**Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics**

2011; 240 pp; Softcover

MSC: Primary 11;

Print ISBN: 978-0-8218-1355-3

Product Code: MMONO/240

Print ISBN: 978-0-8218-1355-3

Product Code: MMONO/240

List Price: $52.00

AMS Member Price: $41.60

MAA Member Price: $46.80

**Electronic ISBN: 978-1-4704-1815-1
Product Code: MMONO/240.E**

List Price: $52.00

AMS Member Price: $41.60

MAA Member Price: $46.80

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#### Supplemental Materials

# Number Theory 2: Introduction to Class Field Theory

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*Kazuya Kato; Nobushige Kurokawa; Takeshi Saito*

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.

#### Reviews & Endorsements

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

#### Table of Contents

# Table of Contents

## Number Theory 2: Introduction to Class Field Theory

- Cover Cover11
- Title page iii4
- Contents v6
- Preface to the English edition vii8
- What is class field theory? 110
- Local and global fields 3342
- 𝜁 (II) 111120
- Class field theory (II) 151160
- Appendix B. Galois theory 215224
- Appendix C. Lights of places 223232
- Answers to questions 227236
- Answers to exercises 231240
- Index 239248
- Back Cover Back Cover1258