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