G. Tenenbaum

collaborators

4 papers

math.NT2026

On integral boxes of minimal surface

Jonathan RotgÃ©, GÃ©rald 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 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

Mean values of arithmetic functions and application to sums of powers

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.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…

On integral boxes of minimal surface

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

Mean values of arithmetic functions and application to sums of powers

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