Amélioration effective du théorème de Liouville
An application of Kronecker's theorem to transcendence theory.
An application of metric diophantine approximation in hyperbolic space to quadratic forms.
For any real τ, a lim sup set WG,y(τ) of τ-(well)-approximable points is defined for discrete groups G acting on the Poincaré model of hyperbolic space. Here y is a 'distinguished point' on the sphere at infinity whose orbit under G corresponds to the rationals (which can be regarded as the orbit of the point at infinity under the modular group) in the classical theory of diophantine approximation.In this paper the Hausdorff dimension of the set WG,y(τ) is determined for geometrically finite groups...
An Application of the Division Theory of Elliptic Functions to Diophantine Approximation.
An approximation property of quadratic irrationals
Let be irrational. Several authors studied the numberswhere is a positive integer and denotes the set of all real numbers of the form with restricted integer coefficients . The value of was determined for many particular Pisot numbers and for the golden number. In this paper the value of is determined for irrational numbers , satisfying with a positive integer .
An arithmetic criterion for the values of the exponential function
An arithmetical theorem on linear forms
An axiomatization of Nesterenko's method and applications on Mahler functions II
An effective lower bound for a certain exponential function
An effective p-adic analogue of a theorem of Thue
An effective Version of Faltings' Product Theorem.
An elementary treatment of a general diophantine problem
An elliptic analogue of the Franklin-Schneider theorem
An ergodic sum related to the approximation by continued fractions.
An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma
An exponential Diophantine equation related to the sum of powers of two consecutive k-generalized Fibonacci numbers
A generalization of the well-known Fibonacci sequence given by F₀ = 0, F₁ = 1 and for all n ≥ 0 is the k-generalized Fibonacci sequence whose first k terms are 0,..., 0, 1 and each term afterwards is the sum of the preceding k terms. For the Fibonacci sequence the formula holds for all n ≥ 0. In this paper, we show that there is no integer x ≥ 2 such that the sum of the xth powers of two consecutive k-generalized Fibonacci numbers is again a k-generalized Fibonacci number. This generalizes...
An extension of a theorem of Duffin and Schaeffer in Diophantine approximation
Duffin and Schaeffer have generalized the classical theorem of Khintchine in metric Diophantine approximation in the case of any error function under the assumption that all the rational approximants are irreducible. This result is extended to the case where the numerators and the denominators of the rational approximants are related by a congruential constraint stronger than coprimality.
An extension of the Khinchin-Groshev theorem
We prove a version of the Khinchin-Groshev theorem in Diophantine approximation for quadratic extensions of function fields in positive characteristic.
An improvement of the quantitative subspace theorem
An inductive method for proving the transcendence of certain series