Critères de non-automaticité et leurs applications
Démonstration probabiliste d'un lemme combinatoire pour l'approximation diophantienne des nombres algébriques
Density of rational points on an algebraic group. (Densité des points rationnels sur un groupe algébrique.)
Density of rational points on an algebraic group. Errata. (Densité des points rationnels sur un groupe algébrique (errata).)
Dépendance d’exponentielles -adiques
Der Überlagerungsradius gewisser algebraischer Kurven und die Werte der Betafunktion an rationalen Stellen.
Diagonales de fractions rationnelles et équations différentielles
Diagonalization and rationalization of algebraic Laurent series
We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is an algebraic power series of degree at most and height at most , where is an effective constant that only depends on...
Dimension algébrique de sous-groupes analytiques de variétés de groupe
Soient une variété de groupe définie sur le corps des nombres algébriques, et un sous-groupe à paramètres de , de dimension algébrique . Nous nous proposons de majorer le rang (sur ) des sous-groupes de dont l’image par est contenue dans le groupe des points algébriques de .E. Bombieri et S. Lang ont déjà obtenu de telles majorations, en supposant que les points de sont très bien distribués : pour , on a pour des variétés linéaires, et pour des variétés abéliennes .Nous...
Diophantine Approximation and Lattices with Complex Multiplication.
Diophantine approximation and special Liouville numbers
This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers . The approach relies on results on the connection between the set of all -adic expansions () of and their associated approximation constants. As an application, explicit construction of real numbers with prescribed approximation properties are deduced and illustrated by Matlab plots.
Diophantine Approximation on Abelian Varieties with Complex Mulitplication.
Diophantine approximation on Veech surfaces
We show that Y. Cheung’s general -continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates in an appropriate sense. The saddle connection continued fractions then allow one to recognize certain transcendental...
Diophantine Approximations of Infinite Series and Products
This survey paper presents some old and new results in Diophantine approximations. Some of these results improve Erdos' results on~irrationality. The results in irrationality, transcendence and linear independence of infinite series and infinite products are put together with idea of irrational sequences and expressible sets.
Diophantine approximations related to rational values of G-functions
Distribution des points de petite hauteur dans les groupes multiplicatifs
We prove a new lower bound for the height of points on a subvariety of a multiplicative torus, which lie outside the union of torsion subvarieties of . Although lower bounds for the heights of these points where already known (decreasing multi-exponential function of the degree for Scmhidt and Bombieri–Zannier, [Sch], [Bo-Za], and inverse monomial in the degree by the second author of this note and P. Philippon, [Da-Phi]), our method provesup to an the sharpest conjectures that can be formulated....
Ein Approximationsmaß für transzendente Lösungen gewisser transzendenter Gleichungen.
Ein p-adischer Beweis für die Irrationalität der Nullstellen von Besselfunktionen.
Einbettungen kommutativer algebraischer Gruppen und einige ihrer Eigenschaften.
Eine arithmetische Eigenschaft der Koeffizienten hypergeometrischer Funktionen mit algebraischen Parametern.