On the mean square of the error term for the two-dimensional divisor   problem (I)
  Suppose $a$ and $b$ are two fixed positive integers such that $(a,b)=1.$ In this paper we shall establish an asymptotic formula for the mean square of the error term $\Delta_{a,b}(x)$ of the general two-dimensional divisor problem. 
Wenguang Zhai, Xiaodong Cao