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  • © 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

  • Includes supplementary material: sn.pub/extras

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

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eBook USD 129.00
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  • ISBN: 978-3-662-03983-0
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Softcover Book USD 169.99
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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

"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

Keywords

  • Algebraic Number Theory
  • Arithmetic Algebraic Geometry
  • File available at Lightning Source
  • algebra
  • number theory

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: 978-3-540-65399-8

  • Softcover ISBN: 978-3-642-08473-7

  • eBook ISBN: 978-3-662-03983-0

  • Series ISSN: 0072-7830

  • Series E-ISSN: 2196-9701

  • Edition Number: 1

  • Number of Pages: XVII, 574

  • Topics: Number Theory

Buying options

eBook USD 129.00
Price excludes VAT (USA)
  • ISBN: 978-3-662-03983-0
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 169.99
Price excludes VAT (USA)
Hardcover Book USD 169.99
Price excludes VAT (USA)