The Theory of Algebraic Number Fields

  • Authors
  • David Hilbert

Table of contents

  1. Front Matter
    Pages I-XXXVI
  2. The Theory of General Number Fields

    1. Front Matter
      Pages 1-1
    2. David Hilbert
      Pages 3-7
    3. David Hilbert
      Pages 9-16
    4. David Hilbert
      Pages 17-23
    5. David Hilbert
      Pages 33-39
    6. David Hilbert
      Pages 41-52
    7. David Hilbert
      Pages 53-64
    8. David Hilbert
      Pages 65-66
    9. David Hilbert
      Pages 67-75
  3. Galois Number Fields

  4. Quadratic Number Fields

    1. Front Matter
      Pages 113-113
    2. David Hilbert
      Pages 115-119
    3. David Hilbert
      Pages 133-147
    4. David Hilbert
      Pages 155-157
  5. Cyclotomic Fields

  6. Kummer Number Fields

  7. Back Matter
    Pages 335-351

About this book


This book is an English translation of Hilbert's Zahlbericht, the monumental report on the theory of algebraic number field which he composed for the German Mathematical Society. In this magisterial work Hilbert provides a unified account of the development of algebraic number theory up to the end of the nineteenth century. He greatly simplified Kummer's theory and laid the foundation for a general theory of abelian fields and class field theory. David Hilbert (1862-1943) made great contributions to many areas of mathematics - invariant theory, algebraic number theory, the foundations of geometry, integral equations, the foundations of mathematics and mathematical physics. He is remembered also for his lecture at the Paris International Congress of Mathematicians in 1900 where he presented a set of 23 problems "from the discussion of which an advancement of science may be expected" - his expectations have been amply fulfilled.


Prime Prime number algebra algebraic number fields algebraische Zahlkörper number theory

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1998
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08306-8
  • Online ISBN 978-3-662-03545-0
  • Buy this book on publisher's site