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"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."--BOOK JACKET. "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."--BOOK JACKET.

Algebraic fields. --- Cyclotomy. --- Algebraic fields --- Cyclotomy --- 511.6 --- 511.6 Algebraic number fields --- Algebraic number fields --- Equations, Cyclotomic --- Number theory --- Equations, Abelian --- Algebraic numbers --- Fields, Algebraic --- Algebra, Abstract --- Algebraic number theory --- Rings (Algebra) --- Number theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra