A lower bound on the mean value of the Erdős-Hooley Delta function

Kevin Ford, Dimitris Koukoulopoulos, Terence Tao

We give an improved lower bound for the average of the Erdős-Hooley function $\Delta (n)$, namely ${\sum }_{n\le x}\Delta (n){\gg }_{\epsilon }x(\log \log x{)}^{1+\eta -\epsilon }$ for all $x\geqslant…