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Cyclotomic Fields I and II (Graduate Texts in Mathematics) (v. 1-2) - Serge Lang
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Serge Lang:
Cyclotomic Fields I and II (Graduate Texts in Mathematics) (v. 1-2) - gebrauchtes Buch

ISBN: 0387966714

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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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Cyclotomic fields: v. 1-2 - Lang, s.
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Cyclotomic fields: v. 1-2 - neues Buch

ISBN: 9780387966717

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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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Cyclotomic Fields I-II - Lang, Serge
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Cyclotomic Fields I-II - gebrauchtes Buch

ISBN: 9780387966717

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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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Cyclotomic Fields I and II - Karl Rubin; Serge Lang
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Karl Rubin; Serge Lang:
Cyclotomic Fields I and II - neues Buch

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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 Versandkosten:zzgl. Versandkosten
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Cyclotomic Fields I and II als Buch von Serge Lang - Serge Lang
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Cyclotomic Fields I and II:2nd ed. 1990. Serge Lang Cyclotomic Fields I and II:2nd ed. 1990. Serge Lang Bücher > Wissenschaft > Mathematik, Springer

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Details zum Buch
Cyclotomic Fields I and II
Autor:

Lang, Serge

Titel:

Cyclotomic Fields I and II

ISBN-Nummer:

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.

Detailangaben zum Buch - Cyclotomic Fields I and II


EAN (ISBN-13): 9780387966717
ISBN (ISBN-10): 0387966714
Gebundene Ausgabe
Erscheinungsjahr: 2007
Herausgeber: Springer-Verlag GmbH
458 Seiten
Gewicht: 0,877 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 28.05.2007 14:44:13
Buch zuletzt gefunden am 12.06.2017 16:06:11
ISBN/EAN: 0387966714

ISBN - alternative Schreibweisen:
0-387-96671-4, 978-0-387-96671-7


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