Cyclotomic Fields I and II / Edition 2

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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.

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Editorial Reviews

Except for the inclusion of an appendix (by Karl Rubin) treating important recent developments having to do with "The Main Conjecture", this is essentially a reprint of a pair of volumes first published in 1978 and 1980. Provides advanced students and mature mathematicians with a clear and authoritative account of some deep material, in some aspects and applications of which there is at present a good deal of lively interest. (NW) Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780387966717
  • Publisher: Springer New York
  • Publication date: 12/1/1989
  • Series: Graduate Texts in Mathematics Series, #121
  • Edition description: 2nd ed. 1990
  • Edition number: 2
  • Pages: 436
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.06 (d)

Table of Contents

Contents: Character Sums.- Stickelberger Ideals and Bernoulli Distributions.- Complex Analytic Class Number Formulas.- The p-adic L-function.- Iwasawa Theory and Ideal Class Groups.- Kummer Theory over Cyclotomic Zp-extensions.- Iwasawa Theory of Local Units.- Lubin-Tate Theory.- Explicit Reciprocity Laws.- Measures and Iwasawa Power Series.- The Ferrero-Washington Theorems.- Measures in the Composite Case.- Divisibility of Ideal Class Numbers.- p-adic Preliminaries.- The Gamma Function and Gauss Sums.- Gauss Sums and the Artin-Schreier Curve.- Gauss Sums as Distributions.- Appendix: The Main Conjecture.- Bibliography.- Index.

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