Multiple Fourier series and lattice point problems

For the multiple Fourier series of periodization some radial functions on Rd, we investigate behavior spherical partial sum. We show Gibbs-Wilbraham phenomenon, Pinsky phenomenon and third for series, involving convergence properties them. The is closely related to lattice point problems, which a classical theme analytic number theory. also prove that, case two or three dimensions, problem equivalent problems in sense. In particular, at origin dimensions Hardy's conjecture Gauss's circle problem.