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Unit Equations in Diophantine Number Theory

AUD$150.00 inc GST

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: January 2016
  • availability: Available
  • format: Hardback
  • isbn: 9781107097605

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About the Authors
  • Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.

    • Presents the state of the art following enormous progress over the past forty years
    • Compiles results previously scattered across the literature
    • An important resource for researchers working in Diophantine number theory
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    Product details

    • Date Published: January 2016
    • format: Hardback
    • isbn: 9781107097605
    • length: 378 pages
    • dimensions: 235 x 158 x 25 mm
    • weight: 0.66kg
    • availability: Available
  • Table of Contents

    Preface
    Summary
    Glossary of frequently used notation
    Part I. Preliminaries:
    1. Basic algebraic number theory
    2. Algebraic function fields
    3. Tools from Diophantine approximation and transcendence theory
    Part II. Unit equations and applications:
    4. Effective results for unit equations in two unknowns over number fields
    5. Algorithmic resolution of unit equations in two unknowns
    6. Unit equations in several unknowns
    7. Analogues over function fields
    8. Effective results for unit equations over finitely generated domains
    9. Decomposable form equations
    10. Further applications
    References
    Index.

  • Authors

    Jan-Hendrik Evertse, Universiteit Leiden
    Jan-Hendrik Evertse is Assistant Professor in the Mathematical Institute at Leiden University. His research concentrates on Diophantine approximation and applications to Diophantine problems. In this area he has obtained some influential results, in particular on estimates for the numbers of solutions of Diophantine equations and inequalities. He has written more than 75 research papers and co-authored one book with Bas Edixhoven entitled Diophantine Approximation and Abelian Varieties (2003).

    Kálmán Győry, Debreceni Egyetem, Hungary
    Kálmán Győry is Professor Emeritus at the University of Debrecen, a member of the Hungarian Academy of Sciences and a well-known researcher in Diophantine number theory. Over his career he has obtained several significant and pioneering results, among others on unit equations, decomposable form equations, and their various applications. His results have been published in one book and 160 research papers. Győry is also the founder and leader of the Number Theory Research Group in Debrecen, which consists of his former students and their descendants.

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