Logarithmic density of a sequence of integers and density of its ratio set

Abstract

L'accès aux archives de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.cedram.org/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

On weighted densities

“…Then both densities can be calculated using the technique in [5], integrating the function x α in the corresponding intervals and cancelling the constant multipliers 1/(α + 1):…”

On estimations of dispersion of ratio block sequences

“…Relations between (R)-density and asymptotic density were studied, among others, in papers [3], [4], [6] and [7]. Now let X = {x 1 , x 2 , .…”

On calculation of generalized densities

“…( [1], [2], [3], [4], [5], [6], [7], [8]). Usually the sets in question are written as infinite union of consecutive blocks of positive integers and there is no general formula for densities of such sets.…”