Higher moments of the error term in the divisor problem

Aleksandar Ivić, Wenguang Zhai

It is proved that, if $k\ge 2$ is a fixed integer and $1\ll H\le X/2$, then $$ \int_{X-H}^{X+H}Δ^4_k(x)\d x \ll_εX^ε\Bigl(HX^{(2k-2)/k} + H^{(2k-3)/(2k+1)}X^{(8k-8)/(2k+1)}\Bigr),…