Number Theory 2: Introduction to Class Field Theory
About this Title
Kazuya Kato, University of Chicago, Chicago, IL, Nobushige Kurokawa, Tokyo Institute of Technology, Tokyo, Japan and Takeshi Saito, University of Tokyo, Tokyo, Japan. Translated by Masato Kuwata
Publication: Translations of Mathematical Monographs
Publication Year: 2011; Volume 240
ISBNs: 978-0-8218-1355-3 (print); 978-1-4704-1815-1 (online)
MathSciNet review: MR2817199
MSC: Primary 11-01; Secondary 11Mxx, 11R37, 11Rxx, 11Sxx
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.
Graduate students and research mathematicians interested in number theory.
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