“…Even for the unit disk in the plane, in which case the problem is the famous Gauss circle problem, we are still far away from the conjectured optimal growth rate. For historical results on the lattice point problem, see for example [10], [17], etc. Motivated by the "eigenvalue optimization among rectangles" problem in spectral geometry, in the paper [1] P. Antunes and P. Freitas studied the following variation of the Gauss circle problem: find the "optimal stretching factor" that maximizes the remainder term #(N 2 ∩ tAB) − πt 2 /4, ( * )where B = B(0, 1) is the unit disk in R 2 , and A = diag(s, s −1 ).…”