A characterization theorem for the $L^2$-discrepancy of integer points in dilated polygons

Giancarlo Travaglini, Maria Rosaria Tupputi

Let $C$ be a convex $d$-dimensional body. If $\rho$ is a large positive number, then the dilated body $\rho C$ contains ${\rho }^d\left|C\right|+\mathcal{O}\left({\rho }^{d-1}\right)$ i…