Introduction to Cyclotomic Fields

  • Lawrence C. Washington

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

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Lawrence C. Washington
    Pages 1-8
  3. Lawrence C. Washington
    Pages 9-19
  4. Lawrence C. Washington
    Pages 20-29
  5. Lawrence C. Washington
    Pages 30-46
  6. Lawrence C. Washington
    Pages 47-86
  7. Lawrence C. Washington
    Pages 87-112
  8. Lawrence C. Washington
    Pages 113-142
  9. Lawrence C. Washington
    Pages 143-166
  10. Lawrence C. Washington
    Pages 167-184
  11. Lawrence C. Washington
    Pages 185-204
  12. Lawrence C. Washington
    Pages 205-231
  13. Lawrence C. Washington
    Pages 232-263
  14. Lawrence C. Washington
    Pages 264-320
  15. Lawrence C. Washington
    Pages 321-331
  16. Lawrence C. Washington
    Pages 332-372
  17. Lawrence C. Washington
    Pages 373-390
  18. Back Matter
    Pages 391-490

About this book

Introduction

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.

Keywords

Calc Calculation Fields Galois theory Kreiskörper Maxima algebra algebraic number theory class congruence functions group number theory testing theorem

Authors and affiliations

  • Lawrence C. Washington
    • 1
  1. 1.Mathematics DepartmentUniversity of MarylandCollege ParkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1934-7
  • Copyright Information Springer-Verlag New York, Inc. 1997
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7346-2
  • Online ISBN 978-1-4612-1934-7
  • Series Print ISSN 0072-5285
  • About this book