Titlebook: Introduction to Cyclotomic Fields; Lawrence C. Washington Textbook 1997Latest edition Springer Science+Business Media New York 1997 Calc.C

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Intercept

Galois Groups Acting on Ideal Class Groups,h underlies the rest of the chapter. As applications, Kummer’s result “ . ” is made more precise and a classical result of Scholz on class groups of quadratic fields is proved. Finally, we show that Vandiver’s conjecture implies that the ideal class group of .is isomorphic to the minus part of the group ring modulo the Stickelberger ideal.

构想

Cyclotomic Fields of Class Number One,presumably too large to make computations feasible. In 1971, Montgomery and Uchida independently obtained much better values of ., from which it followed that.Masley was then able to use this information, plus a table of . for ø. ≤ 256, to explicitly determine all . with .=1.

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Textbook 1997Latest editionaic 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 edi

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0072-5285 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

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0072-5285 iving other recent developments, including primality testing via Jacobi sums and Sinnott‘s proof of the vanishing of Iwasawa‘s f-invariant.978-1-4612-7346-2978-1-4612-1934-7Series ISSN 0072-5285 Series E-ISSN 2197-5612

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