A constructive approach to Kronecker approximations and its application to the Mertens conjecture.
A method in diophantine approximation V
A note on Diophantine approximation.
A note on |αp - q|
A relative Dobrowolski lower bound over abelian extensions
A remark on the theory of Diophantine approximations (Preliminary communication)
A rigidity phenomenon for the Hardy-Littlewood maximal function
The Hardy-Littlewood maximal function ℳ and the trigonometric function sin x are two central objects in harmonic analysis. We prove that ℳ characterizes sin x in the following way: Let be a periodic function and α > 1/2. If there exists a real number 0 < γ < ∞ such that the averaging operator has a critical point at r = γ for every x ∈ ℝ, then f(x) = a + bsin(cx+d) for some a,b,c,d ∈ ℝ. This statement can be used to derive a characterization of trigonometric functions as those nonconstant...
Approximations diophantiennes et eutaxie
Bounding squares in second order recurrence sequences
Complex dimensions of self-similar fractal strings and Diophantine approximation.
Concordant sequences and integral-valued entire functions
A classic theorem of Pólya shows that the function is the “smallest” integral-valued entire transcendental function. A variant due to Gel’fond applies to entire functions taking integral values on a geometric progression of integers, and Bézivin has given a generalization of both results. We give a sharp formulation of Bézivin’s result together with a further generalization.
Correction to the paper "Divergent trajectories of flows on homogeneous spaces and Diophantine approximations".
Critère de reconnaissabilité de fonctions analytiques et fonctions entières arithmétiques
Diophantine approximation involving primes.
Diophantine approximations on projective spaces.
Divergent trajectories of flows on homogeneous spaces and Diophantine approximation.
Dividing rational points on abelian varieties of CM-type
Dyson's lemma for products of two curves of arbitrary genus.
Fonctions entières prenant des valeurs entières
Fonctions entieres prenant des valeurs entieres ainsi que ses derivees sur des suites recurrentes binaires.