The lattice point discrepancy of a body of revolution: Improving the lower bound by Soundararajan?s method

Abstract

Abstract.For a convex body B in R 3 which is invariant under rotations around one coordinate axis and has a smooth boundary of bounded nonzero curvature, the lattice point discrepancy P B (t) (number of integer points minus volume) of a linearly dilated copy √ tB is estimated from below. On the basis of a recent method of K. Soundararajan [16] an Ω -bound is obtained that improves upon all earlier results of this kind.

A mean-square bound for the lattice discrepancy of bodies of rotation with flat points on the boundary

“…while the papers by M. Kühleitner [20] and M. Kühleitner and W. G. Nowak [21] provided Ω-results. A recent article of E. Krätzel and W. G. Nowak [19] gives a version of (2.1) with numerical constants, for the special case of an ellipsoid.…”

“…while papers by M. Kühleitner [20] and M. Kühleitner and W.G. Nowak [21] provided Ω -results. A recent article of E. Krätzel and W.G.…”