All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 18 Next

Displaying 341 – 360 of 1536

Showing per page

Diagonalization and rationalization of algebraic Laurent series

Boris Adamczewski, Jason P. Bell (2013)

Annales scientifiques de l'École Normale Supérieure

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 p the reduction modulo p of the diagonal of a multivariate algebraic power series f with integer coefficients is an algebraic power series of degree at most p A and height at most A p A , where A is an effective constant that only depends on...

Dimension algébrique de sous-groupes analytiques de variétés de groupe

Michel Waldschmidt (1975)

Annales de l'institut Fourier

Soient G une variété de groupe définie sur le corps Q ‾ des nombres algébriques, et φ : C n → G C un sous-groupe à n paramètres de G , de dimension algébrique d . Nous nous proposons de majorer le rang ℓ (sur Z ) des sous-groupes Γ de C n dont l’image par φ est contenue dans le groupe G Q ‾ des points algébriques de G .E. Bombieri et S. Lang ont déjà obtenu de telles majorations, en supposant que les points de Γ sont très bien distribués : pour d ≥ n + 1 , on a ℓ ≤ n 2 + 3 n pour des variétés linéaires, et ℓ ≤ 2 n 2 + 4 n pour des variétés abéliennes .Nous...

Dimension of countable intersections of some sets arising in expansions in non-integer bases

David Färm, Tomas Persson, Jörg Schmeling (2010)

Fundamenta Mathematicae

We consider expansions of real numbers in non-integer bases. These expansions are generated by β-shifts. We prove that some sets arising in metric number theory have the countable intersection property. This allows us to consider sets of reals that have common properties in a countable number of different (non-integer) bases. Some of the results are new even for integer bases.

Diophantine approximation and special Liouville numbers

Johannes Schleischitz (2013)

Communications in Mathematics

This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers ζ 1 , ζ 2 , ... , ζ k . The approach relies on results on the connection between the set of all s -adic expansions ( s ≥ 2 ) of ζ 1 , ζ 2 , ... , ζ k and their associated approximation constants. As an application, explicit construction of real numbers ζ 1 , ζ 2 , ... , ζ k with prescribed approximation properties are deduced and illustrated by Matlab plots.

Diophantine approximation in Banach spaces

Lior Fishman, David Simmons, Mariusz Urbański (2014)

Journal de Théorie des Nombres de Bordeaux

In this paper, we extend the theory of simultaneous Diophantine approximation to infinite dimensions. Moreover, we discuss Dirichlet-type theorems in a very general framework and define what it means for such a theorem to be optimal. We show that optimality is implied by but does not imply the existence of badly approximable points.

Currently displaying 341 – 360 of 1536