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ISBN: 0387966714

ID: 7676913

Kummer's work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the success of this general theory has tended to obscure special facts proved by Kummer about cyclotomic fields which lie deeper than the general theory. For a long period in the 20th century this aspect of Kummer's work seems to have been largely forgotten, except for a few papers, among which are those by Pollaczek [Po], Artin-Hasse [A-H] and Vandiver [Va]. In the mid 1950's, the theory of cyclotomic fields was taken up again by Iwasawa and Leopoldt. Iwasawa viewed cyclotomic fields as being analogues for number fields of the constant field extensions of algebraic geometry, and wrote a great sequence of papers investigating towers of cyclotomic fields, and more generally, Galois extensions of number fields whose Galois group is isomorphic to the additive group of p-adic integers. Leopoldt concentrated on a fixed cyclotomic field, and established various p-adic analogues of the classical complex analytic class number formulas. In particular, this led him to introduce, with Kubota, p-adic analogues of the complex L-functions attached to cyclotomic extensions of the rationals. Finally, in the late 1960's, Iwasawa [Iw 11] made the fundamental discovery that there was a close connection between his work on towers of cyclotomic fields and these p-adic L-functions of Leopoldt - Kubota. algebra,algebra and trigonometry,mathematics,number theory,pure mathematics,science and math,science and math,textbooks Mathematics, Springer

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ISBN: 9780387966717

ID: 9cf0a4307c28452b1b1f7719b264e0fe

Kummers work on cyclotomic fields paved the way for the development of algebraic number theory in general by Dedekind, Weber, Hensel, Hilbert, Takagi, Artin and others. However, the success of this general theory has tended to obscure special facts proved by Kummer about cyclotomic fields which lie deeper than the general theory. For a long period in the 20th century this aspect of Kummers work seems to have been largely forgotten, except for a few papers, among which are those by Pollaczek [Po], Artin-Hasse [A-H] and Vandiver [Va]. In the mid 1950s, the theory of cyclotomic fields was taken up again by Iwasawa and Leopoldt. Iwasawa viewed cyclotomic fields as being analogues for number fields of the constant field extensions of algebraic geometry, and wrote a great sequence of papers investigating towers of cyclotomic fields, and more generally, Galois extensions of number fields whose Galois group is isomorphic to the additive group of p-adic integers. Leopoldt concentrated on a fixed cyclotomic field, and, [PU: Springer]

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ISBN: 9780387966717

ID: 1187025

This book is a combined edition of the books previously published as "Cyclotomic Fields, Vol. I and II." It continues to provide a basic introduction to the theory of these number fields, which are of great interest in classical number theory, as well as in other areas, such as K-theory. Cyclotomic Fields begins with basic material on character sums, and proceeds to treat class number formulas, p-adic L-functions, Iwasawa theory, Lubin-Tate theory, and explicit reciprocity laws, and the Ferrero-Washington theorems, which prove Iwasawa's conjecture on the growth of the p-primary part of the ideal class group. Cyclotomic Fields I-II Lang, Serge, Springer

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ISBN: 9780387966717

ID: 9780387966717

Mathematics; Number Theory Cohomology, Prime, algebra, finite field, homomorphism, number theory Books Book, Springer Science+Business Media

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Combining the works previously published as Cyclotomic Fields, V. I & II, this book introduces these number fields, which are of great interest in classical number theory and other areas such as K-theory. Covers p-adic L-functions, Iwasawa theory, and mor Shipping costs:zzgl. Versandkosten, plus shipping costs
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1989, ISBN: 9780387966717

ID: 1176437

[ED: 2], 2nd ed. 1990, Hardcover, Buch, [PU: Springer-Verlag New York Inc.]

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Title: | ## Cyclotomic Fields I and II |

ISBN: |

** Details of the book - Cyclotomic Fields I and II**

EAN (ISBN-13): 9780387966717

ISBN (ISBN-10): 0387966714

Hardcover

Publishing year: 2007

Publisher: Springer-Verlag GmbH

458 Pages

Weight: 0,877 kg

Language: eng/Englisch

Book in our database since 28.05.2007 14:44:13

Book found last time on 11.07.2017 13:15:05

ISBN/EAN: 0387966714

ISBN - alternate spelling:

0-387-96671-4, 978-0-387-96671-7

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