6 papers · 1 filter
On local laws for the number of small prime factors
Gérald Tenenbaum
Investigating a question of Alladi, we describe the local distribution of small prime factors of integers, with emphasis on the transition phase occurring for certain values of the…
Moyennes effectives de fonctions multiplicatives complexes
Gérald Tenenbaum
We establish effective mean-value estimates for a wide class of multiplicative arithmetic functions, thereby providing (essentially optimal) quantitative versions of Wirsing's clas…
Remarks on the Selberg--Delange method
Régis de la Bretèche, Gérald Tenenbaum
Let be a complex number and let be a multiplicative arithmetic function whose Dirichlet series takes the form , where is associated to a multi…
Note on a conjecture of Hildebrand regarding friable integers
Régis de la Bretèche, Gérald Tenenbaum
Hildebrand proved that the smooth approximation for the number of -friable integers not exceeding holds for under the Riemann hypothes…
Friable averages of complex arithmetic functions
Régis de la Bretèche, Gérald Tenenbaum
We evaluate friable averages of arithmetic functions whose Dirichlet series is analytically close to some complex power of the Riemann zeta function. We obtain asymptotic expansion…
Friable averages of oscillating multiplicative functions
Régis de la Bretèche, Gérald Tenenbaum
We evaluate friable averages of arithmetic functions whose Dirichlet series is analytically close to some negative power of the Riemann zeta function. We obtain asymptotic expansio…