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Product Details
This is Volume 83 in Springer's Graduate Texts in Mathematics series. From the back cover: "Starting at an elementary level, the volume coversp -adicL -functions, class numbers, cyclotomic units, Fermat's Last Theorem, and Iwasawa's theory ofZp -extensions, leading the reader to an understanding of modern research literature. Many exercises are included.
"The second edition includes a new chapter on the work of Thaine, Kolyvagin, and Rubin, including a proof of the Main Conjecture. There is also a chapter giving other recent developments, including primality testing via Jacobi sums and Sinnott's proof of the vanishing of Iwasawa's μ-invariant."
BRIEF CONTENTS
Preface to the Second Edition
Preface to the First Edition
Chapter 1. Fermat's Last Theorem
Chapter 2. Basic Results
Chapter 3. Dirichlet Characters
Chapter 4. Dirichlet L-series and Class Number Formulas
Chapter 5. p-adic L-functions and Bernoulli Numbers
Chapter 6. Stickelberger's Theorem
Chapter 7. Iwasawa's Construction of p-adic L-functions
Chapter 8. Cyclotomic Units
Chapter 9. The Second Case of Fermat's Last Theorem
Chapter 10. Galois Groups Acting on Ideal Class Groups
Chapter 11. Cyclotomic Fields of Class Number One
Chapter 12. Measures and Distributions
Chapter 13. Iwasawa's Theory of Zp-extensions
Chapter 14. The Kronecker-Weber Theorem
Chapter 15. The Main Conjecture and Annihilation of Class Groups
