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Diophantine Approximation

Festschrift for Wolfgang Schmidt

  • Conference proceedings
  • © 2008

Overview

Editors:
  1. Hans Peter Schlickewei

    1. Philipps-Universität Marburg, Marburg, Germany

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  2. Klaus Schmidt

    1. Universität Wien, Vienna, Austria

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  3. Robert F. Tichy

    1. Technische Universität Graz, Graz, Austria

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  • Current information on important branches of diophantine approximation from leading experts in the field
  • Diverse methods are presented
  • The influence of diophantine approximation in other fields, e.g. combinatorial geometry, game theory
  • Includes supplementary material: sn.pub/extras

Part of the book series: Developments in Mathematics (DEVM)

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Table of contents (23 papers)

  1. Front Matter

    Pages i-vii
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  2. The Mathematical Work of Wolfgang Schmidt

    • Hans Peter Schlickewei
    Pages 1-20

  3. SchÄffer’s Determinant Argument

    • Roger C. Baker
    Pages 21-39

  4. Arithmetic Progressions and Tic-Tac-Toe Games

    • József Beck
    Pages 41-93

  5. Metric Discrepancy Results for Sequences {nkx} and Diophantine Equations

    • István Berkes, Walter Philipp, Robert F. Tichy
    Pages 95-105

  6. Mahler’s Classification of Numbers Compared with Koksma’s, II

    • Yann Bugeaud
    Pages 107-121

  7. Rational Approximations to A q-Analogue of π and Some Other q-Series

    • Peter Bundschuh, Wadim Zudilin
    Pages 123-139

  8. Orthogonality and Digit Shifts in the Classical Mean Squares Problem in Irregularities of Point Distribution

    • William W. L. Chen, Maxim M. Skriganov
    Pages 141-159

  9. Applications of the Subspace Theorem to Certain Diophantine Problems

    • Pietro Corvahja, Umberto Zannier
    Pages 161-174

  10. A Generalization of the Subspace Theorem With Polynomials of Higher Degree

    • Jan-Hendrik Evertse, Roberto G. Ferretti
    Pages 175-198

  11. On the Diophantine Equation G n (x) = G m (y) with Q (x, y)=0

    • Clemens Fuchs, Attila Pethő, Robert F. Tichy
    Pages 199-209

  12. A Criterion for Polynomials to Divide Infinitely Many k- Nomials

    • Lajos Hajdu, Robert Tijdeman
    Pages 211-220

  13. Approximants de Padé des q-Polylogarithmes

    • Christian Krattenthaler, Tanguy Rivoal
    Pages 221-230

  14. The Set of Solutions of Some Equation for Linear Recurrence Sequences

    • Viktor Losert
    Pages 231-235

  15. Counting Algebraic Numbers with Large Height I

    • David Masser, Jeffrey D. Vaaler
    Pages 237-243

  16. Class Number Conditions for the Diagonal Case of the Equation of Nagell and Ljunggren

    • Preda Mihăilescu
    Pages 245-273

  17. Construction of Approximations to Zeta-Values

    • Yuri V. Nesterenko
    Pages 275-293

  18. Quelques Aspects Diophantiens des VariéTés Toriques Projectives

    • Patrice Philippon, Martín Sombra
    Pages 295-338

  19. Une Inégalité de Łojasiewicz Arithmétique

    • Gaël Rémond
    Pages 339-345

  20. On the Continued Fraction Expansion of a Class of Numbers

    • Damien Roy
    Pages 347-361
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Keywords

About this book

This volume contains 22 research and survey papers on recent developments in the field of diophantine approximation. The first article by Hans Peter Schlickewei is devoted to the scientific work of Wolfgang Schmidt. Further contributions deal with the subspace theorem and its applications to diophantine equations and to the study of linear recurring sequences. The articles are either in the spirit of more classical diophantine analysis or of geometric or combinatorial flavor. In particular, estimates for the number of solutions of diophantine equations as well as results concerning congruences and polynomials are established. Furthermore, the volume contains transcendence results for special functions and contributions to metric diophantine approximation and to discrepancy theory. The articles are based on lectures given at a conference at the Erwin Schr6dinger Institute in Vienna in 2003, in which many leading experts in the field of diophantine approximation participated. The editors are very grateful to the Erwin Schr6dinger Institute and to the FWF (Austrian Science Fund) for the financial support and they express their particular thanks to Springer-Verlag for the excellent cooperation. Robert E Tichy Diophantine Approximation H. E Schlickewei et al. , Editors 9 Springer-Verlag 2008 THE MATHEMATICAL WORK OF WOLFGANG SCHMIDT Hans Peter Schlickewei Mathematik Informatik, und Philipps-Universitiit Hans-Meerwein-Strasse, Marburg, 35032 Marburg, Germany k. Introduction Wolfgang Schmidt's mathematical activities started more than fifty years ago in 1955. In the meantime he has written more than 180 papers - many of them containing spectacular results and breakthroughs in different areas of number theory.

Editors and Affiliations

  • Philipps-Universität Marburg, Marburg, Germany

    Hans Peter Schlickewei

  • Universität Wien, Vienna, Austria

    Klaus Schmidt

  • Technische Universität Graz, Graz, Austria

    Robert F. Tichy

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