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Birkhäuser

Diophantine Equations and Power Integral Bases

New Computational Methods

  • Book
  • © 2002

Overview

Authors:
  1. István Gaál

    1. Institute of Mathematics and Informatics, University of Debrecen, Hungary

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Introduction

    • István Gaál
    Pages 1-5

  3. Auxiliary Results, Tools

    • István Gaál
    Pages 7-17

  4. Auxiliary Equations

    • István Gaál
    Pages 19-44

  5. Index Form Equations in General

    • István Gaál
    Pages 45-52

  6. Cubic Fields

    • István Gaál
    Pages 53-54

  7. Quartic Fields

    • István Gaál
    Pages 55-77

  8. Quintic Fields

    • István Gaál
    Pages 79-95

  9. Sextic Fields

    • István Gaál
    Pages 97-112

  10. Relative Power Integral Bases

    • István Gaál
    Pages 113-127

  11. Some Higher Degree Fields

    • István Gaál
    Pages 129-147

  12. Tables

    • István Gaál
    Pages 149-170

  13. Back Matter

    Pages 171-184
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Keywords

About this book

This monograph investigates algorithms for determining power integral bases in algebraic number fields. It introduces the best-known methods for solving several types of diophantine equations using Baker-type estimates, reduction methods, and enumeration algorithms. Particular emphasis is placed on properties of number fields and new applications. The text is illustrated with several tables of various number fields, including their data on power integral bases. Good resource for solving classical types of diophantine equations. Aimed at advanced undergraduate/graduate students and researchers.

Authors and Affiliations

  • Institute of Mathematics and Informatics, University of Debrecen, Hungary

    István Gaál

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