R. de la Bretèche

activity

20192022

most citedTwo upper bounds for the Erdős--Hooley Delta-function

1 citations · 1 across the 1 of their papers we have counts for

collaborators

3 papers

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{\…

math.PR2020

On strong and almost sure local limit theorems for a probabilistic model of the Dickman distribution

Régis de la Bretèche, Gérald Tenenbaum

Let ${Z_{k}}_{k ⩾ 1}$ denote a sequence of independent Bernoulli random variables defined by $P (Z_{k} = 1) = 1/ k = 1 - P (Z_{k} = 0)$ $(k ⩾ 1)$ and put $T_n:=\su…

math.NT2019

Small Gál sums and applications

Régis de la Bretèche, Marc Munsch, Gérald Tenenbaum

In recent years, maximizing Gál sums regained interest due to a firm link with large values of $L$ -functions. In the present paper, we initiate an investigation of small sums of Gá…