4 citations · 4 across the 5 of their papers we have counts for
9 papers
Moyennes de certaines fonctions multiplicatives sur les entiers friables, 3
Gérald Tenenbaum, Jie Wu
We consider logarithmic averages, over friable integers, of non-negative multiplicative functions. Under logarithmic, one-sided or two-sided hypotheses, we obtain sharp estimates t…
Sur le biais d'une loi de probabilité relative aux entiers friables
Gérald Tenenbaum
The standard probability law on the set of -friable integers not exceeding assigns to each friable integer a probability proportional to where $α=α(x,y)…
Entiers ultrafriables en progressions arithmétiques
Cécile Dartyge, David Feutrie, Gérald Tenenbaum
A natural integer is called -ultrafriable if none of the prime powers occurring in its canonical decomposition exceed . We investigate the distribution of -ultrafriable in…
Remarques sur une somme liée à la fonction de Möbius
Régis de la Bretèche, François Dress, Gérald Tenenbaum
For integer and real number , define where denotes the Möbius function. Put ${\cal L}(y):=\exp\left\{(\log…
Somme des chiffres et changement de base
Régis de la Bretèche, Thomas Stoll, Gérald Tenenbaum
Let denote the sum of digits of an integer in the base expansion. Answering, in a extended form, a question of Deshouillers, Habsieger, Laishram, and Landreau, we…
Sommes de Gál et applications
Régis de la Bretèche, Gérald Tenenbaum
We evaluate the asymptotic size of various sums of Gál type, in particular where is a finite s…
Note sur les lois locales conjointes de la fonction nombre de facteurs premiers
Gérald Tenenbaum
Let and let denote distinct irreducible polynomials with integer coefficients. We show that, for vectors with coordinates not exceedin…
Inégalité de Turán-Kubilius friable et indépendance asymptotique
Régis de la Bretèche, Youness Lamzouri, Gérald Tenenbaum
Elaborating on previous works and taking advantage of estimates on the local behaviour of the counting function of friable integers, we determine the optimal range in which the fri…
Lois de répartition des diviseurs des entiers friables
Sary Drappeau, Gérald Tenenbaum
According to a general probabilistic principle, the natural divisors of friable integers (i.e.~free of large prime factors) should normally present a Gaussian distribution. We show…