Spherical sums in the sphere problem

Here is given an analytical expression for the error term of the asymptotic formula for the number of lattice points in the sphere using a spherical trigonometric sum, that is triple sum over lattice points lying on the sphere of variable radius. Conclusion based on a threefold application of the one-dimensional Poisson summation formula with the error term. The estimation of the error term is held in an explicit form.