5 citations · 8 across the 11 of their papers we have counts for
15 papers
D{é}monstration d'une conjecture de Kruyswijk et Meijer sur le plus petit d{é}nominateur des nombres rationnels d'un intervalle
Michel Balazard, Bruno Martin
The average value of the smallest denominator of a rational number belonging to the interval , where~, is proved to be asymptotically equivalent to~$16…
Autour d'un problème extrémal étudié par Edmund Landau
Michel Balazard
This expository article is an introduction to Landau's problem of bounding the derivative, knowing bounds for the function and its second derivative, and some of its variants and g…
Sur le minimum de la fonction de Brjuno
Michel Balazard, Bruno Martin
The Brjuno function attains a strict global minimum at the golden section.
Sur la variation de certaines suites de parties fractionnaires
Michel Balazard, Leila Benferhat, Mihoub Bouderbala
Let . We prove the following asymptotic formula with $c=b…
Fonctions arithmétiques multiplicativement monotones
Michel Balazard
A real arithmetic function f is multiplicatively monotonous if f (mn) -- f (m) has constant sign for m, n positive integers. Properties and examples of such functions are discussed…
Sur certaines équations fonctionnelles approchées, liées à la transformation de Gauss
Michel Balazard, Bruno Martin
In the line of classical work by Hardy, Littlewood and Wilton, we study a class of functional equations involving the Gauss transformation from the theory of continued fractions. T…