Introduction to cyclotomic fields
By: Lawrence C. Washington.
Edition: 2nd ed.
Series: Graduate texts in mathematics ;; 83
Publisher: Springer
Published: 1997
Place of publication: New York
Language: eng
Number of pages: 487
Subjects: Algebraic fields; Cyclotomy
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[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.
Notes: Includes bibliographical references (p. 424-482) and index.