Aproximace reálných čísel a příspěvek českých matematiků. (1. část)
Aproximace reálných čísel a příspěvek českých matematiků. (2. část)
Automatic continued fractions are transcendental or quadratic
We establish new combinatorial transcendence criteria for continued fraction expansions. Let be an algebraic number of degree at least three. One of our criteria implies that the sequence of partial quotients of is not ‘too simple’ (in a suitable sense) and cannot be generated by a finite automaton.
Best simultaneous diophantine approximations of Pisot numbers and Rauzy fractals
Best simultaneous diophantine approximations of some cubic algebraic numbers
Let be a real algebraic number of degree over whose conjugates are not real. There exists an unit of the ring of integer of for which it is possible to describe the set of all best approximation vectors of .’
Contributions to Diophantine Approximation in Fields of Series.
Correct rounding of algebraic functions
We explicit the link between the computer arithmetic problem of providing correctly rounded algebraic functions and some diophantine approximation issues. This allows to get bounds on the accuracy with which intermediate calculations must be performed to correctly round these functions.
Courbes elliptiques, fonctions L , et tours cyclotomiques.
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.
Effective approximation of algebraic numbers, d'après Enrico Bombieri
Effective diophantine approximation on