4. V. Guillemin, ”Riemann-Roch for toric orbifolds”, J. Differential Geom. 45 (1997), p. 53–73.

Summary: “It is well known that theN-th Riemann sum of a compactly supported function on the real line converges to the Riemann integral at a much faster rate than the standard O(1/N) rate of convergence if the sum is over the lattice, Z/N. In this paper we prove an n-dimensional version of this result for Riemann sums over polytopes.