Classical Diophantine Equations

  • Authors
  • Vladimir G. Sprindžuk
  • Editors
  • Ross Talent
Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1559)

Table of contents

  1. Front Matter
    Pages I-XIII
  2. Vladimir G. Sprindžuk
    Pages 1-13
  3. Vladimir G. Sprindžuk
    Pages 14-29
  4. Vladimir G. Sprindžuk
    Pages 30-60
  5. Vladimir G. Sprindžuk
    Pages 61-84
  6. Vladimir G. Sprindžuk
    Pages 85-110
  7. Vladimir G. Sprindžuk
    Pages 111-137
  8. Vladimir G. Sprindžuk
    Pages 138-154
  9. Vladimir G. Sprindžuk
    Pages 155-187
  10. Vladimir G. Sprindžuk
    Pages 188-218
  11. Back Matter
    Pages 219-232

About this book

Introduction

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over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded.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.

Keywords

Algebraic Number Theory Arithmetic Geometry Class Number Diophantine Equation Diophantine approximation

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0073786
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-57359-3
  • Online ISBN 978-3-540-48083-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book