$L^p$ and Weak-$L^p$ estimates for the number of integer points in translated domains

Abstract

Revisiting and extending a recent result of M.Huxley, we estimate the $L^p\left({\mathbb{T}}^d\right)$ and Weak-$L^p\left({\mathbb{T}}^d\right)$ norms of the discrepancy between the volume and the number of integer points in translated domains.

Cited by in corpus (3)

• Mixed $L^p(L^2)$ norms of the lattice point discrepancy
• $L^p$ norms of the lattice point discrepancy
• Higher Moments for Lattice Point Discrepancy of Convex Domains and Annuli