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Lectures on the Theory of Algebraic Numbers

  • Textbook
  • © 1981

Overview

Authors:
  1. Erich Hecke

    1. Department of Mathematics, Universität Hamburg, Hamburg, Federal Republic of Germany

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 77)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xii
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  2. Elements of Rational Number Theory

    • Erich Hecke
    Pages 1-15

  3. Abelian Groups

    • Erich Hecke
    Pages 16-39

  4. Abelian Groups in Rational Number Theory

    • Erich Hecke
    Pages 40-53

  5. Algebra of Number Fields

    • Erich Hecke
    Pages 54-67

  6. General Arithmetic of Algebraic Number Fields

    • Erich Hecke
    Pages 68-138

  7. Introduction of Transcendental Methods into the Arithmetic of Number Fields

    • Erich Hecke
    Pages 139-154

  8. The Quadratic Number Field

    • Erich Hecke
    Pages 155-194

  9. The Law of Quadractic Reciprocity in Arbitrary Number Fields

    • Erich Hecke
    Pages 195-237

  10. Back Matter

    Pages 238-242
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Keywords

About this book

. . . if one wants to make progress in mathematics one should study the masters not the pupils. N. H. Abel Heeke was certainly one of the masters, and in fact, the study of Heeke L­ series and Heeke operators has permanently embedded his name in the fabric of number theory. It is a rare occurrence when a master writes a basic book, and Heeke's Lectures on the Theory of Algebraic Numbers has become a classic. To quote another master, Andre Weil: "To improve upon Heeke, in a treatment along classical lines of the theory of algebraic numbers, would be a futile and impossible task. " We have tried to remain as close as possible to the original text in pre­ serving Heeke's rich, informal style of exposition. In a very few instances we have substituted modern terminology for Heeke's, e. g. , "torsion free group" for "pure group. " One problem for a student is the lack of exercises in the book. However, given the large number of texts available in algebraic number theory, this is not a serious drawback. In particular we recommend Number Fields by D. A. Marcus (Springer-Verlag) as a particularly rich source. We would like to thank James M. Vaughn Jr. and the Vaughn Foundation Fund for their encouragement and generous support of Jay R. Goldman without which this translation would never have appeared. Minneapolis George U. Brauer July 1981 Jay R.

Authors and Affiliations

  • Department of Mathematics, Universität Hamburg, Hamburg, Federal Republic of Germany

    Erich Hecke

Bibliographic Information

  • Book Title: Lectures on the Theory of Algebraic Numbers

  • Authors: Erich Hecke

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4757-4092-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1981

  • Hardcover ISBN: 978-0-387-90595-2Published: 04 December 1981

  • Softcover ISBN: 978-1-4419-2814-6Published: 03 December 2010

  • eBook ISBN: 978-1-4757-4092-9Published: 09 March 2013

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XII, 242

  • Topics: Number Theory

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