A Hardy-type result on the average of the lattice point error term over long intervals

Burton Randol

Suppose $D$ is a suitably admissible compact subset of ${\mathbb{R}}^k$ having a smooth boundary with possible zones of zero curvature. Let \mbox{$R(T,θ,x)= N(T,θ,x) - T^{k}\mathrm{v…