  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.
