Diophantine Approximation

1. Front Matter

   Pages i-vii

   PDF

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

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.

• Algebra
• Diophantine
• Diophantine approximation
• Festschrift
• Number Theory
• Tichy
• Wolfgang Schmidt
• continued fraction

• Philipps-Universität Marburg, Marburg, Germany

  Hans Peter Schlickewei

• Universität Wien, Vienna, Austria

  Klaus Schmidt

• Technische Universität Graz, Graz, Austria

  Robert F. Tichy

Policies and ethics