On the mean square of the error term for the number of lattice points in a two-dimensional area

Lirui Jia, Wenguang Zhai

Suppose $a,b$ are fixed algebraic numbers with $1\le a<b$. Let ${\Delta }_{a,b}(x)$ be the error term for the number of lattice points in a two-dimensional area $h^a{r}^b\le x$ with $h,…