On the friable mean-value of the Erdős-Hooley Delta function

Bruno Martin, Gérald Tenenbaum, Julie Wetzer

For integer $n$ and real $u$, define $\Delta (n,u):=|\{d:d\mid n,{\mathrm{e}}^u<d⩽{\mathrm{e}}^{u+1}\}|$. Then, put $\Delta (n):={\max }_{u\in \mathbb{R}}\Delta (n,u).$ We provide uniform uppe…