Distribution of integral lattice points in an ellipsoid with a diophantine center

Abstract

We evaluate the mean square limit of exponential sums related to a rational ellipsoid, extending a work of Marklof. Moreover, as a result of it, we study the asymptotic values of the normalized deviations of the number of lattice points inside a rational ellipsoid and inside a rational thin ellipsoidal shell. (C) 2015 Elsevier Inc. All rights reserved.