On some mean value results for the zeta-function and a divisor problem

Aleksandar Ivic

Let $\Delta (x)$ denote the error term in the classical Dirichlet divisor problem, and let the modified error term in the divisor problem be ${\Delta }^{\ast }(x)=-\Delta (x)+2\Delta (2x)-\frac{1}{2}\Delta (4x)$.…