Let $\Omega$ be a convex set in $R^d$ which contains $0$ in its interior and let $N(t)$ be the number of points with integer coordinates in the dilate $t \Omega$. $N(t)$ is asymptotic to $t^d |\Omega|$ as $t\to \infty$ and we discuss estimates for the error term $E(t)=N(t)-t^d|\Omega|$. In particular we report on sharp bounds for mean square discrepancies (joint work with A. Iosevich and E. Sawyer).
Copyright. All Rights Reserved.