R. Bretèche

collaborators

5 papers

math.NT2026

Random Multiplicative Functions and Making Squares from Polynomial Values

RÃ©gis de la BretÃ¨che, Victor Y. Wang, Max Wenqiang Xu

For a large family of polynomials $P (X) \in Z [X]$ , we prove central limit theorems for $\sum_{n \leq N} f (P (n))$ for both Rademacher and extended Rademacher multiplicative fu…

math.NT2025

On moments of the ErdÅs--Hooley Delta-function

R. de la BretÃ¨che, G. Tenenbaum

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

math.NT2025

Remarks on the Selberg--Delange method

RÃ©gis de la BretÃ¨che, GÃ©rald Tenenbaum

Let $ϱ$ be a complex number and let $f$ be a multiplicative arithmetic function whose Dirichlet series takes the form $I^¶ (s)^{ϱ} G (s)$ , where $G$ is associated to a multi…

math.NT2025

Note on a conjecture of Hildebrand regarding friable integers

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

math.NT2025

Note on the mean value of the ErdÅs--Hooley Delta-function

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

Random Multiplicative Functions and Making Squares from Polynomial Values

On moments of the ErdÅs--Hooley Delta-function

Remarks on the Selberg--Delange method

Note on a conjecture of Hildebrand regarding friable integers

Note on the mean value of the ErdÅs--Hooley Delta-function

On moments of the ErdÅs--Hooley Delta-function

Note on the mean value of the ErdÅs--Hooley Delta-function