On metric theorems in the theory of uniform distribution
As promised in the first paper of this series (Ann. Inst. Fourier, 26-4 (1976), 115-131), these two articles deal with the asymptotic distribution of the fractional parts of where is an arithmetical function (namely , , ) and is an integer (or a prime order) running over the interval . The results obtained are rather sharp, although one can improve on some of them at the cost of increased technicality. Number-theoretic applications will be given later on.
Étude de l’ensemble des réels tels que soit une suite “mal répartie”, étant une suite donnée. Si est assez dense, cet ensemble est dénombrable.