R. Bretèche

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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

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

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…

math.NT2024

Friable averages of complex arithmetic functions

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…

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

Friable averages of complex arithmetic functions

On moments of the ErdÅs--Hooley Delta-function

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