Lattice Points in Large Convex Bodies

Integer points close to convex surfaces

“…Hlawka [8] obtained a general dimensional asymptotic formula, which in three dimensions yields an error of size (1); see also Krätzel [13]. Under the C ∞ hypothesis of a convergent Taylor series, the error term in the asymptotic formula has been improved, most recently by Müller [18].…”

“…In Müller [18] the differential inequality assumed is that the Gaussian curvature does not vanish. We can regard (3) as a corresponding quantitative bound.…”

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

“…These are due to W. Müller [14] (who improved earlier results by E. Hlawka [5] and Krätzel and Nowak [10], [11]), and the second named author [15], respectively.…”

The lattice point discrepancy of a torus in ℝ3

“…An alternative proof of this result can be found as Satz 5.15 in E. Krätzel's book [11]. By some very hard analysis, W. Müller [16] managed to rene this estimate up to P B (t) = O t 63/43+ε .…”