A Banach space determined by the Weil height
A Markoff-Type Chain for the View-Obstruction Problem for Spheres in R4.
A note on two linear forms
We prove a result on approximations to a real number θ by algebraic numbers of degree ≤ 2 in the case when we have certain information about the uniform Diophantine exponent ω̂ for the linear form x₀ + θx₁ + θ²x₂.
A note to a bifurcation result of H. Kielhöfer for the wave equation
A modification of a classical number-theorem on Diophantine approximations is used for generalizing H. kielhöfer's result on bifurcations of nontrivial periodic solutions to nonlinear wave equations.
A powerful determinant.
An arithmetical theorem on linear forms
An improvement of the quantitative subspace theorem
An isoperimetric inequality for the area of plane regions defined by binary forms
Anwendung des Perron'schen Beweises eines Satzes von Minkowski
Approximation diophantienne dans les corps de séries en plusieurs variables
Nous montrons ici un théorème d’approximation diophantienne entre le corps des séries formelles en plusieurs variables et son complété pour la topologie de Krull.
Approximations diophantiennes des nombres sturmiens
Nous établissons pour tout nombre sturmien (de développement dyadique sturmien) des propriétés d'approximation diophantienne très précises, ne dépendant que de l'angle de la suite sturmienne, généralisant ainsi des travaux antérieurs de Ferenczi-Mauduit et Bullett-Sentenac.
Constants for lower bounds for linear forms in the logarithms of algebraic numbers II. The homogeneous rational case
Constants for lower bounds for linear forms in the logarithms of algebraic numbers I. The general case
Continued fraction expansions for complex numbers-a general approach
We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the absolute values...
Corrigendum to the paper "Constants for lower bounds for linear forms in the logarithms of algebraic numbers II. The homogeneous rational case" (Acta Arith. 55 (1990), 15-22)
Counting problems and semisimple groups.
Diophantine approximation with primes and powers of two.
Diophantine approximations related to rational values of G-functions
Diophantine approximations with Fibonacci numbers
Let be the -th Fibonacci number. Put . We prove that the following inequalities hold for any real :1) ,2) ,3) .These results are the best possible.
Diophantine equations with linear recurrences An overview of some recent progress
We shall discuss some known problems concerning the arithmetic of linear recurrent sequences. After recalling briefly some longstanding questions and solutions concerning zeros, we shall focus on recent progress on the so-called “quotient problem” (resp. "-th root problem"), which in short asks whether the integrality of the values of the quotient (resp. -th root) of two (resp. one) linear recurrences implies that this quotient (resp. -th root) is itself a recurrence. We shall also relate such...