The lattice discrepancy of certain three-dimensional bodies

作者：Kraetzel Ekkehard; Nowak Werner Georg^*

来源：Monatshefte fur Mathematik, 2011, 163(2): 149-174.

DOI：10.1007/s00605-010-0226-8

• Lattice points
• Lattice discrepancy
• Convex bodies
• Exponential sums

Based on a very precise approximation to the lattice discrepancy of a Lam, disc, an asymptotic formula is established for the number of lattice points in the three-dimensional body
vertical bar u(1)vertical bar(mk) + (vertical bar u(2)vertical bar(k) + vertical bar u(3)vertical bar(k))(m) oe <= x(mk) ,
for large real x and fixed reals m, k. Particular attention is paid to the boundary points of Gaussian curvature zero.

• 出版日期2011-6