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Diophantine Approximation

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 28 – July 6, 2000

  • David Masser
  • Yuri V. Nesterenko
  • Hans Peter Schlickewei
  • Wolfgang Schmidt
  • Michel Waldschmidt
  • Francesco Amoroso
  • Umberto Zannier

Part of the Lecture Notes in Mathematics book series (LNM, volume 1819)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Yuri Nesterenko
    Pages 53-106
  3. Hans Peter Schlickewei
    Pages 107-170
  4. Wolfgang M. Schmidt
    Pages 171-247
  5. Back Matter
    Pages 345-351

About this book

Introduction

Diophantine Approximation is a branch of Number Theory having its origins intheproblemofproducing“best”rationalapproximationstogivenrealn- bers. Since the early work of Lagrange on Pell’s equation and the pioneering work of Thue on the rational approximations to algebraic numbers of degree ? 3, it has been clear how, in addition to its own speci?c importance and - terest, the theory can have fundamental applications to classical diophantine problems in Number Theory. During the whole 20th century, until very recent times, this fruitful interplay went much further, also involving Transcend- tal Number Theory and leading to the solution of several central conjectures on diophantine equations and class number, and to other important achie- ments. These developments naturally raised further intensive research, so at the moment the subject is a most lively one. This motivated our proposal for a C. I. M. E. session, with the aim to make it available to a public wider than specialists an overview of the subject, with special emphasis on modern advances and techniques. Our project was kindly supported by the C. I. M. E. Committee and met with the interest of a largenumberofapplicants;forty-twoparticipantsfromseveralcountries,both graduatestudentsandseniormathematicians,intensivelyfollowedcoursesand seminars in a friendly and co-operative atmosphere. The main part of the session was arranged in four six-hours courses by Professors D. Masser (Basel), H. P. Schlickewei (Marburg), W. M. Schmidt (Boulder) and M. Waldschmidt (Paris VI). This volume contains expanded notes by the authors of the four courses, together with a paper by Professor Yu. V.

Keywords

Diophantine approximation Linear Forms in Logarithms Number Theory algebra equation proof

Authors and affiliations

  • David Masser
    • 1
  • Yuri V. Nesterenko
    • 2
  • Hans Peter Schlickewei
    • 3
  • Wolfgang Schmidt
    • 4
  • Michel Waldschmidt
    • 5
  1. 1.Institute of MathematicsBasel UniversityBaselSwitzerland
  2. 2.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  3. 3.Department of MathematicsPhillips University of MarburgMarburgGermany
  4. 4.Department of MathematicsUniversity of ColoradoBoulderUSA
  5. 5.Institut de MathématiquesUniversité Paris VIParisFrance

Editors and affiliations

  • Francesco Amoroso
    • 1
  • Umberto Zannier
    • 2
  1. 1.Laboratoire de Mathématiques Nicolas Oresme, CNRS UMR 6139Université de CaenCaenFrance
  2. 2.Instituto Universitario Architettura-D.C.A.VeneziaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-44979-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2003
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-40392-0
  • Online ISBN 978-3-540-44979-9
  • Series Print ISSN 0075-8434
  • Buy this book on publisher's site
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