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Classical Diophantine Equations

  • Book
  • © 1993

Overview

Authors:
  1. Vladimir G. Sprindžuk
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    You can also search for this author in PubMed   Google Scholar

Editors:
  1. Ross Talent
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1559)

Part of the book sub series: LOMI and Euler International Mathematical Institute, St.Petersburg (3157)

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Origins

    • Vladimir G. Sprindžuk
    Pages 1-13

  3. Algebraic foundations

    • Vladimir G. Sprindžuk
    Pages 14-29

  4. Linear forms in the logarithms of algebraic numbers

    • Vladimir G. Sprindžuk
    Pages 30-60

  5. The Thue equation

    • Vladimir G. Sprindžuk
    Pages 61-84

  6. The Thue-Mahler equation

    • Vladimir G. Sprindžuk
    Pages 85-110

  7. Elliptic and hyperelliptic equations

    • Vladimir G. Sprindžuk
    Pages 111-137

  8. Equations of hyperelliptic type

    • Vladimir G. Sprindžuk
    Pages 138-154

  9. The class number value problem

    • Vladimir G. Sprindžuk
    Pages 155-187

  10. Reducibility of polynomials and diophantine equations

    • Vladimir G. Sprindžuk
    Pages 188-218

  11. Back Matter

    Pages 219-232
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Keywords

About this book

The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, now that the book appears in English, close studyand emulation. In particular those emphases allow him to devote the eighth chapter to an analysis of the interrelationship of the class number of algebraic number fields involved and the bounds on the heights of thesolutions of the diophantine equations. Those ideas warrant further development. The final chapter deals with effective aspects of the Hilbert Irreducibility Theorem, harkening back to earlier work of the author. There is no other congenial entry point to the ideas of the last two chapters in the literature.

Bibliographic Information

  • Book Title: Classical Diophantine Equations

  • Authors: Vladimir G. Sprindžuk

  • Editors: Ross Talent

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0073786

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Softcover ISBN: 978-3-540-57359-3Published: 20 December 1993

  • eBook ISBN: 978-3-540-48083-9Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XII, 236

  • Additional Information: Original Russian edition published by Nauka, Moscow 1982

  • Topics: Number Theory

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