Démonstration du théorème de Baker-Feldman via les formes linéaires en deux logarithmes
Nous montrons que l’inégalité de Liouville-Baker-Feldman est une conséquence facile d’une minoration de formes linéaires en deux logarithmes.
Démonstration probabiliste d'un lemme combinatoire pour l'approximation diophantienne des nombres algébriques
Determinants in the study of Thue's method and curves with prescribed singularities.
Die p-adische Verallgemeinerung des Satzes von Thue-Siegel-Roth-Schmidt.
Diophantine approximation and deformation
Diophantine approximation with partial sums of power series
We study the question: How often do partial sums of power series of functions coalesce with convergents of the (simple) continued fractions of the functions? Our theorems quantitatively demonstrate that the answer is: not very often. We conjecture that in most cases there are only a finite number of partial sums coinciding with convergents. In many of these cases, we offer exact numbers in our conjectures.
Diophantine equations with products of consecutive terms in Lucas sequences II
Dyson's lemma and a theorem of Esnault and Viehweg.
Dyson's Lemma for polynomials in several variables (and the Theorem of Roth).
Dyson's lemma for products of two curves of arbitrary genus.