Introduction to Cyclotomic Fields
By L.C. Washington
* Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
* Number Of Pages: 389
* Publication Date: 1982-12-31
* ISBN-10 / ASIN: 3540906223
* ISBN-13 / EAN: 9783540906223
Book Description:
Introduction to Cyclotomic Fields is a carefully written exposition of a central area of number theory that can be used as a second course in algebraic number theory. Starting at an elementary level, the volume covers p-adic L-functions, class numbers, cyclotomic units, Fermat's Last Theorem, and Iwasawa's theory of Z_p-extensions, leading the reader to an understanding of modern research literature. Many exercises are included.
The second edition includes a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture. There is also a chapter giving other recent developments, including primality testing via Jacobi sums and Sinnott's proof of the vanishing of Iwasawa's f-invariant.
Summary: Extraordinarily Comprensive Review
Rating: 5
This book has pretty much anything you could want about the theory of cyclotomic fields: Fermat's Last Theorem(See how it was done before Wiles!), an introduction to iwasawa theory, and a proof of Thaine's theorem for those of you who are interested in Mihailescu's proof of Catalan's conjecture. One thing though, this book is not really an introduction. If you're not familiar with Algebraic Number Theory and p-adic analysis, you will be completely lost in this book. It definitely doesn't hurt to know at least the major statements of Class Field Theory. Other than that, though, a truly great book!
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