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Iwanami Series in Modern Mathematics
Number Theory 2: Introduction to Class Field Theory
Kazuya Kato, University of Chicago, IL, Nobushige Kurokawa, Tokyo Institute of Technology, Japan, and Takeshi Saito, University of Tokyo, Japan

Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics
2011; 240 pp; softcover
Volume: 240
ISBN-10: 0-8218-1355-2
ISBN-13: 978-0-8218-1355-3
List Price: US$52
Member Price: US$41.60
Order Code: MMONO/240
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See also:

Number Theory 1: Fermat's Dream - Kazuya Kato, Nobushige Kurokawa and Takeshi Saito

Number Theory 3: Iwasawa Theory and Modular Forms - Nobushige Kurokawa, Masato Kurihara and Takeshi Saito

Elliptic Curves, Modular Forms, and Their L-functions - Alvaro Lozano-Robledo

Class Field Theory - Emil Artin and John Tate

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.

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Graduate students and research mathematicians interested in number theory.


"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

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