Effektive Abschaetzungen fuer den Gitterrest gewisser ebener und dreidimensionaler Bereiche

Abstract

Effective estimates for the lattice point discrepancy of certain planar and three-dimensional domains. This paper provides estimates, with explicit constants, for the lattice point discrepancy of o-symmetric ellipse discs and ellipsoids in three-dimensional Euclidean space, as well as of three-dimensional convex bodies which are invariant under rotations around one coordinate axis and have a smooth boundary of finite nonzero Gaussian curvature throughout.