Higher Moments for Lattice Point Discrepancy of Convex Domains and Annuli

Xiaorun Wu

Given a domain $\Omega \subseteq {\mathbb{R}}^2$, let $\mathcal{D}(\Omega ,x,R)$ be the number of lattice points from ${\mathbb{Z}}^2$ in $R\Omega -x$, for $R\ge 1$ and $x\in {\mathbb{T}}^2$, minus the a…