Sur la variation quadratique totale de la suite des parties fractionnaires des quotients d'un nombre réel positif par les nombres entiers naturels consécutifs

We give an asymptotic formula for the quadratic total variation of the sequence of fractional parts of the quotients of a positive real number by the consecutive natural numbers

Sur la variation totale de la suite des parties fractionnaires des quotients d'un nombre r{\'e}el positif par les nombres entiers naturels cons{\'e}cutifs

We give an asymptotic formula for the total variation of the sequence of fractional parts of the quotients of a positive real number by the consecutive natural numbers.Comment: in French, A para\^itre au (to appear in) Moscow Journal of Combinatorics and Number Theor

Comportement local moyen de la fonction de Brjuno

We describe the average behaviour of the Brjuno function in the neighbourhood of any given point of the unit interval. In particular, we show that its Lebesgue set is the set of Brjuno numbers and we fi nd the asymptotic behaviour of the modulus of continuity of its integral.Comment: A para\^itre dans Fundamenta Mathematica