Introduction to Cyclotomic Fields (Graduate Texts in Mathematics) - Hardcover

Washington, Lawrence C.

Hardcover

ISBN 10: 0387906223 ISBN 13: 9780387906225

Publisher: Springer Verlag, 1982

Synopsis

This text on a central area of number theory covers p-adic L-functions, class numbers, cyclotomic units, Fermat’s Last Theorem, and Iwasawa’s theory of Z_p-extensions. This edition contains a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture, as well as a chapter on other recent developments, such as primality testing via Jacobi sums and Sinnott’s proof of the vanishing of Iwasawa’s f-invariant.

About this title

From the Back Cover

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(subscript 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 (mu)-invariant.

Review

The job done by the author will surely be valued highly by everyone, whether student or scholar, working in algebraic number theory. -- T Metsnkyl, Mathematical Reviews, issue 97h

Edition details

• Publisher: Springer Verlag
• Publication date: 1982
• Language: English
• ISBN 10: 0387906223
• ISBN 13: 9780387906225
• Binding: Hardcover
• Edition number: 1
• Number of pages: 389