Introduction to class field theory
Author(s)
Bibliographic Information
Introduction to class field theory
（Translations of mathematical monographs, v. 240 . Number theory ; 2）（Iwanami series in modern mathematics）
American Mathematical Society, c2011
- Other Title
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数論. 2 : 類体論とは
Sūron
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Note
"Originally published in Japanese by Iwanami Shoten, publishers, Tokyo, 1998"--T.p. verso
Original Japanese ed. published as no. 19 in the series: 岩波講座現代数学の基礎
Includes index
Description and Table of Contents
Description
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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