Lattice Points in Large Convex Bodies

 Denote by the number of points of the lattice in the “blown up” domain , where is a convex body in () whose boundary is smooth and has nonzero curvature throughout. It is proved that for every fixed where for and . This improves a classic result of E. Hlawka 8] and its refinements due to E. Kr?tzel and W. G. Nowak (14], 15]). The proof uses a multidimensional variant of the method of van der Corput for the estimation of exponential sums. Received 28 August 1998