Synopses & Reviews
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.
Synopsis
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 more.
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.