Introduction to Cyclotomic Fields
By: by Lawrence C. Washington
Edition: Second edition.
Series: Graduate Texts in Mathematics, 0072-5285 -- 83; Graduate texts in mathematics -- 83.
Publisher: Springer New York; Imprint; Springer
Published: 1997
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 487
ISBN-13: 9781461219347
Subjects: Mathematics; Number theory
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.