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Chebyshevskii Sb., 2013, Volume 14, Issue 2, Pages 33–49 (Mi cheb268)  

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.

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UDC: 511.32
Received: 01.03.2013

Citation: L. G. Arkhipova, “Spherical sums in the sphere problem”, Chebyshevskii Sb., 14:2 (2013), 33–49

Citation in format AMSBIB
\Bibitem{Ark13}
\by L.~G.~Arkhipova
\paper Spherical sums in the sphere problem
\jour Chebyshevskii Sb.
\yr 2013
\vol 14
\issue 2
\pages 33--49
\mathnet{http://mi.mathnet.ru/cheb268}


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