Geodesic
Spherical sums in the sphere problem
Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 33-49

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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. 
@article{CHEB_2013_14_2_a3,
     author = {L. G. Arkhipova},
     title = {Spherical sums in the sphere problem},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {33--49},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2013_14_2_a3/}
}
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L. G. Arkhipova. Spherical sums in the sphere problem. Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 33-49. http://geodesic.mathdoc.fr/item/CHEB_2013_14_2_a3/