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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 hypothesi…
An Erdős-Kac theorem for integers with dense divisors
Gérald Tenenbaum, Andreas Weingartner
We show that for large integers , whose ratios of consecutive divisors are bounded above by an arbitrary constant, the number of prime factors follows an approximate normal dist…
Two upper bounds for the Erdős--Hooley Delta-function
Régis de la Bretèche, Gérald Tenenbaum
For integer and real , let . The Erdős--Hooley Delta-function is then defined by $Δ(n):=\max_{u\in{\…
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…