Introduction to Cyclotomic Fields / Edition 2

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Overview

This text on a central area of number theory covers p-adic L-functions, class numbers, cyclotomic units, Fermat’s Last Theorem, and Iwasawa’s theory of Z_p-extensions. This edition contains a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture, as well as a chapter on other recent developments, such as primality testing via Jacobi sums and Sinnott’s proof of the vanishing of Iwasawa’s f-invariant.

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Product Details

  • ISBN-13: 9780387947624
  • Publisher: Springer New York
  • Publication date: 12/5/1996
  • Series: Graduate Texts in Mathematics Series , #83
  • Edition description: 2nd ed. 1997
  • Edition number: 2
  • Pages: 490
  • Product dimensions: 1.19 (w) x 6.14 (h) x 9.21 (d)

Table of Contents

Preface to the Second Edition
Preface to the First Edition
Ch. 1 Fermat's Last Theorem 1
Ch. 2 Basic Results 9
Ch. 3 Dirichlet Characters 20
Ch. 4 Dirichlet L-series and Class Number Formulas 30
Ch. 5 p-adic L-functions and Bernoulli Numbers 47
Ch. 6 Stickelberger's Theorem 87
Ch. 7 Iwasawa's Construction of p-adic L-functions 113
Ch. 8 Cyclotomic Units 143
Ch. 9 The Second Case of Fermat's Last Theorem 167
Ch. 10 Galois Groups Acting on Ideal Class Groups 185
Ch. 11 Cyclotomic Fields of Class Number One 205
Ch. 12 Measures and Distributions 232
Ch. 13 Iwasawa's Theory of Z[subscript p]-extensions 264
Ch. 14 The Kronecker-Weber Theorem 321
Ch. 15 The Main Conjecture and Annihilation of Class Groups 332
Ch. 16 Miscellany 373
Appendix 391
Tables 407
Bibliography 424
List of Symbols 483
Index 485
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