Diophantine Approximation : Festschrift for Wolfgang Schmidt / edited by Hans Peter Schlickewei, Klaus Schmidt, Robert F. Tichy.

Springer eBooks

The Mathematical Work of Wolfgang Schmidt -- SchÄffer’s Determinant Argument -- Arithmetic Progressions and Tic-Tac-Toe Games -- Metric Discrepancy Results for Sequences {nkx} and Diophantine Equations -- Mahler’s Classification of Numbers Compared with Koksma’s, II -- Rational Approximations to A q-Analogue of ? and Some Other q-Series -- Orthogonality and Digit Shifts in the Classical Mean Squares Problem in Irregularities of Point Distribution -- Applications of the Subspace Theorem to Certain Diophantine Problems -- A Generalization of the Subspace Theorem With Polynomials of Higher Degree -- On the Diophantine Equation G n (x) = G m (y) with Q (x, y)=0 -- A Criterion for Polynomials to Divide Infinitely Many k- Nomials -- Approximants de Padé des q-Polylogarithmes -- The Set of Solutions of Some Equation for Linear Recurrence Sequences -- Counting Algebraic Numbers with Large Height I -- Class Number Conditions for the Diagonal Case of the Equation of Nagell and Ljunggren -- Construction of Approximations to Zeta-Values -- Quelques Aspects Diophantiens des VariéTés Toriques Projectives -- Une Inégalité de ?ojasiewicz Arithmétique -- On the Continued Fraction Expansion of a Class of Numbers -- The Number of Solutions of a Linear Homogeneous Congruence -- A Note on Lyapunov Theory for Brun Algorithm -- Orbit Sums and Modular Vector Invariants -- New Irrationality Results for Dilogarithms of Rational Numbers.

This volume contains 21 research and survey papers on recent developments in the field of diophantine approximation. This includes contributions to Wolfgang Schmidt's 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 flavour. Several articles deal with estimates for the number of solutions of diophantine equations as well as with congruences and polynomials. Furthermore, the volume contains transcendence results for special functions and contributions to metric diophantine approximation and discrepancy theory. The articles are based on lectures given at a conference at the Erwin Schrödinger-Institute (Vienna, 2003), where many leading experts in the field of diophantine approximation participated.

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