Sign changes of the error term in the Piltz divisor problem

Siegfred Baluyot, Cruz Castillo

We study the function $Δ_k(x):=\sum_{n\leq x} d_k(n) - \mbox{Res}_{s=1} ( ζ^k(s) x^s/s )$, where $k\ge 3$ is an integer, $d_k(n)$ is the $k$-fold divisor function, and $\zeta (s)$ is t…