G. Tenenbaum

activity

20232026

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4 papers · 1 filter

math.NT2026

On integral boxes of minimal surface

Jonathan Rotgé, Gérald Tenenbaum

Generalising the two-dimensional case, we provide estimates for the mean-values of the lengths of the edges of an integral box with given volume and minimal surface.

math.NT2025

On moments of the Erdős--Hooley Delta-function

R. de la Bretèche, G. 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.NT2024

Mean values of arithmetic functions and application to sums of powers

Régis de la Bretèche, Gérald Tenenbaum

We provide new upper bounds for sums of certain arithmetic functions in many variables at polynomial arguments and, exploiting recent progress on the mean-value of the Erd\H os-Hoo…

math.NT2023

Note on the mean value of 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{\…