Lattice points in bodies of rotation with a dent

Abstract

In the sense of the theory of lattice points in large bodies, a fairly general body of rotation [Formula: see text] in [Formula: see text] is considered whose convexity is being hampered by a “dent” (see Fig. 1). It turns out that, for [Formula: see text] a large real parameter, the true order of magnitude of the lattice discrepancy of [Formula: see text] essentially can be evaluated, contrary to the convex case.