Algebraic Number Theory

  • Frazer┬áJarvis

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Frazer Jarvis
    Pages 17-37
  3. Frazer Jarvis
    Pages 39-63
  4. Frazer Jarvis
    Pages 65-86
  5. Frazer Jarvis
    Pages 87-112
  6. Frazer Jarvis
    Pages 113-147
  7. Frazer Jarvis
    Pages 149-168
  8. Frazer Jarvis
    Pages 169-189
  9. Frazer Jarvis
    Pages 191-206
  10. Frazer Jarvis
    Pages 207-230
  11. Frazer Jarvis
    Pages 231-255
  12. Back Matter
    Pages 257-292

About this book


The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic.

Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform.

The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the first time that the number field sieve has been considered in a textbook at this level.


Algebraic Number Theory Class Groups Number Field Sieve Quadratic Fields Unique Factorisation

Authors and affiliations

  • Frazer┬áJarvis
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of SheffieldSheffieldUnited Kingdom

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-07544-0
  • Online ISBN 978-3-319-07545-7
  • Series Print ISSN 1615-2085
  • Series Online ISSN 2197-4144
  • About this book