© 1999

Algebraic Number Theory


  • The author's enthusiasm for this topic is rarely as evident for the reader as in this book. - A good book, a beautiful book."

  • F. Lorenz in: Deutsche Mathematiker Vereinigung, 1995


Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 322)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Jürgen Neukirch
    Pages 1-97
  3. Jürgen Neukirch
    Pages 99-181
  4. Jürgen Neukirch
    Pages 183-260
  5. Jürgen Neukirch
    Pages 261-315
  6. Jürgen Neukirch
    Pages 317-355
  7. Jürgen Neukirch
    Pages 357-417
  8. Jürgen Neukirch
    Pages 419-549
  9. Back Matter
    Pages 551-574

About this book


"The present book has as its aim to resolve a discrepancy in the textbook literature and ... to provide a comprehensive introduction to algebraic number theory which is largely based on the modern, unifying conception of (one-dimensional) arithmetic algebraic geometry. ... Despite this exacting program, the book remains an introduction to algebraic number theory for the beginner... The author discusses the classical concepts from the viewpoint of Arakelov theory.... The treatment of class field theory is ... particularly rich in illustrating complements, hints for further study, and concrete examples.... The concluding chapter VII on zeta-functions and L-series is another outstanding advantage of the present textbook.... The book is, without any doubt, the most up-to-date, systematic, and theoretically comprehensive textbook on algebraic number field theory available." W. Kleinert in Z.blatt f. Math., 1992 "The author's enthusiasm for this topic is rarely as evident for the reader as in this book. - A good book, a beautiful book." F. Lorenz in Jber. DMV 1995 "The present work is written in a very careful and masterly fashion. It does not show the pains that it must have caused even an expert like Neukirch. It undoubtedly is liable to become a classic; the more so as recent developments have been taken into account which will not be outdated quickly. Not only must it be missing from the library of no number theorist, but it can simply be recommended to every mathematician who wants to get an idea of modern arithmetic." J. Schoissengeier in Montatshefte Mathematik 1994


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Authors and affiliations

  1. 1.RegensburgGermany

Bibliographic information

  • Book Title Algebraic Number Theory
  • Authors Jürgen Neukirch
  • Series Title Grundlehren der mathematischen Wissenschaften
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1999
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-65399-8
  • Softcover ISBN 978-3-642-08473-7
  • eBook ISBN 978-3-662-03983-0
  • Series ISSN 0072-7830
  • Edition Number 1
  • Number of Pages XVII, 574
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
  • Buy this book on publisher's site
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