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  • © 1999

Algebraic Number Theory

Authors:

  • 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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xvii
  2. Algebraic Integers

    • Jürgen Neukirch
    Pages 1-97
  3. The Theory of Valuations

    • Jürgen Neukirch
    Pages 99-181
  4. Riemann-Roch Theory

    • Jürgen Neukirch
    Pages 183-260
  5. Abstract Class Field Theory

    • Jürgen Neukirch
    Pages 261-315
  6. Local Class Field Theory

    • Jürgen Neukirch
    Pages 317-355
  7. Global Class Field Theory

    • Jürgen Neukirch
    Pages 357-417
  8. Zeta Functions and L-series

    • Jürgen Neukirch
    Pages 419-549
  9. Back Matter

    Pages 551-574

About this book

From the review: "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: Zentralblatt für Mathematik, 1992

Authors and Affiliations

  • Regensburg, Germany

    Jürgen Neukirch

Bibliographic Information

  • Book Title: Algebraic Number Theory

  • Authors: Jürgen Neukirch

  • Series Title: Grundlehren der mathematischen Wissenschaften

  • DOI: https://doi.org/10.1007/978-3-662-03983-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: The Editor(s) (if applicable) and The Author(s) 1999

  • Hardcover ISBN: 978-3-540-65399-8Published: 21 May 1999

  • Softcover ISBN: 978-3-642-08473-7Published: 15 December 2010

  • eBook ISBN: 978-3-662-03983-0Published: 14 March 2013

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XVII, 574

  • Topics: Number Theory

Buy it now

Buying options

eBook USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access