Spherical sums in the sphere problem

L. G. Arkhipova

M. V. Lomonosov Moscow State University

Abstract: 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.

Keywords: Sphere problem, spherical sums, exponential sums.

UDC: 511.32

Received: 01.03.2013