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Introduction to Cyclotomic Fields

  • Textbook
  • © 1997

Overview

Authors:
  1. Lawrence C. Washington

    1. Mathematics Department, University of Maryland, College Park, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 83)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Fermat’s Last Theorem

    • Lawrence C. Washington
    Pages 1-8

  3. Basic Results

    • Lawrence C. Washington
    Pages 9-19

  4. Dirichlet Characters

    • Lawrence C. Washington
    Pages 20-29

  5. Dirichlet L-series and Class Number Formulas

    • Lawrence C. Washington
    Pages 30-46

  6. p-adic L-functions and Bernoulli Numbers

    • Lawrence C. Washington
    Pages 47-86

  7. Stickelberger’s Theorem

    • Lawrence C. Washington
    Pages 87-112

  8. Iwasawa’s Construction of p-adic L-functions

    • Lawrence C. Washington
    Pages 113-142

  9. Cyclotomic Units

    • Lawrence C. Washington
    Pages 143-166

  10. The Second Case of Fermat’s Last Theorem

    • Lawrence C. Washington
    Pages 167-184

  11. Galois Groups Acting on Ideal Class Groups

    • Lawrence C. Washington
    Pages 185-204

  12. Cyclotomic Fields of Class Number One

    • Lawrence C. Washington
    Pages 205-231

  13. Measures and Distributions

    • Lawrence C. Washington
    Pages 232-263

  14. Iwasawa’s Theory of ℤ-extensions

    • Lawrence C. Washington
    Pages 264-320

  15. The Kronecker—Weber Theorem

    • Lawrence C. Washington
    Pages 321-331

  16. The Main Conjecture and Annihilation of Class Groups

    • Lawrence C. Washington
    Pages 332-372

  17. Miscellany

    • Lawrence C. Washington
    Pages 373-390

  18. Back Matter

    Pages 391-490
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Keywords

About this book

Introduction to Cyclotomic Fields is a carefully written exposition of a central area of number theory that can be used as a second course in algebraic number theory. Starting at an elementary level, the volume covers p-adic L-functions, class numbers, cyclotomic units, Fermat's Last Theorem, and Iwasawa's theory of Z_p-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 f-invariant.

Authors and Affiliations

  • Mathematics Department, University of Maryland, College Park, USA

    Lawrence C. Washington

Bibliographic Information

  • Book Title: Introduction to Cyclotomic Fields

  • Authors: Lawrence C. Washington

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-1934-7

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1997

  • Hardcover ISBN: 978-0-387-94762-4Published: 05 December 1996

  • Softcover ISBN: 978-1-4612-7346-2Published: 27 September 2012

  • eBook ISBN: 978-1-4612-1934-7Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 2

  • Number of Pages: XIV, 490

  • Topics: Number Theory

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