Number Theory 2: Introduction to Class Field Theory (Translations of Mathematical Monographs)

K. Kato

ISBN 10: 0821813552 / ISBN 13: 9780821813553

Published by American Mathematical Society, 2011

About this Item

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Bibliographic Details

• Title: Number Theory 2: Introduction to Class Field Theory (Translations of Mathematical Monographs)
• Publisher: American Mathematical Society
• Publication Date: 2011
• Language: English
• ISBN 10: 0821813552
• ISBN 13: 9780821813553
• Binding: paperback
• Condition: Good

About this title

Synopsis

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.

About the Author

Kazuya Kato is at the University of Chicago, IL||Nobushige Kurokawa is at the Tokyo Institute of Technology, Japan|Takeshi Saito is at the University of Tokyo, Japa