
Number Theory 2
Introduction to Class Field Theory
American Mathematical Society (Publisher)
Published on 30. October 2011
Book
Paperback/Softback
240 pages
978-0-8218-1355-3 (ISBN)
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.
Reviews / Votes
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 ReviewsMore details
Series
Language
English
Place of publication
Providence
United States
Target group
College/higher education
Weight
305 gr
ISBN-13
978-0-8218-1355-3 (9780821813553)
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Schweitzer Classification
Persons
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, Japan.
Nobushige Kurokawa is at the Tokyo Institute of Technology, Japan.
Takeshi Saito is at the University of Tokyo, Japan.