G. Tenenbaum

activity

20062023

most citedFriable averages of oscillating multiplicative functions

2 citations · 6 across the 16 of their papers we have counts for

collaborators

23 papers

math.NT2023

On the friable mean-value of the Erdős-Hooley Delta function

Bruno Martin, Gérald Tenenbaum, Julie Wetzer

For integer $n$ and real $u$ , define $Δ (n, u) := ∣ {d : d ∣ n, e^{u} < d ⩽ e^{u + 1}} ∣$ . Then, put $Δ (n) := max_{u \in R} Δ (n, u) .$ We provide uniform uppe…

math.NT2023

On simply normal numbers with digit dependencies

Verónica Becher, Agustín Marchionna, Gérald Tenenbaum

Given an integer $b ⩾ 2$ and a set $P$ of prime numbers, the set $T_{P}$ of Toeplitz numbers comprises all elements of $[0, b [$ whose digits $(a_{n})_{n ⩾ 1}$ in the base…

math.NT2023

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…

math.NT2022

Note on a conjecture of Hildebrand regarding friable integers

Régis de la Bretèche, Gérald Tenenbaum

Hildebrand proved that the smooth approximation for the number $Ψ (x, y)$ of $y$ -friable integers not exceeding $x$ holds for $y > (lo g x)^{2 + ε}$ under the Riemann hypothesi…

math.NT2022

An Erdős-Kac theorem for integers with dense divisors

Gérald Tenenbaum, Andreas Weingartner

We show that for large integers $n$ , whose ratios of consecutive divisors are bounded above by an arbitrary constant, the number of prime factors follows an approximate normal dist…

math.NT2022★ 1 cited

Two upper bounds for the Erdős--Hooley Delta-function

Régis de la Bretèche, Gérald Tenenbaum

For integer $n ⩾ 1$ and real $u$ , let $Δ (n, u) := ∣ {d : d ∣ n, e^{u} < d ⩽ e^{u + 1}} ∣$ . The Erdős--Hooley Delta-function is then defined by $Δ(n):=\max_{u\in{\…