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Zap. Nauchn. Sem. POMI, 2013, Volume 418, Pages 198–220 (Mi znsl5723)  

This article is cited in 2 scientific papers (total in 2 papers)

Lattice points in the circle and the sphere

O. M. Fomenko

St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

Abstract: Let $P(x)$ and $P_3(x)$ be the error terms in the Gaussian circle problem and the sphere problem, respectively.
We investigate the asymptotic behavior of the sums
$$ \sum_{\substack{k\le x
k\equiv0\pmod p}}P(k),\quad\sum_{\substack{k\le x
k\equiv0\pmod p}}P_3(k). $$
Here $p\ge2$ is a prime number.

Key words and phrases: Gaussian circle problem, sphere problem, asymptotic behavior.

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English version:
Journal of Mathematical Sciences (New York), 2014, 200:5, 632–645

UDC: 511.466+517.863
Received: 22.09.2013

Citation: O. M. Fomenko, “Lattice points in the circle and the sphere”, Analytical theory of numbers and theory of functions. Part 28, Zap. Nauchn. Sem. POMI, 418, POMI, St. Petersburg, 2013, 198–220; J. Math. Sci. (N. Y.), 200:5 (2014), 632–645

Citation in format AMSBIB
\Bibitem{Fom13}
\by O.~M.~Fomenko
\paper Lattice points in the circle and the sphere
\inbook Analytical theory of numbers and theory of functions. Part~28
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 418
\pages 198--220
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5723}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 200
\issue 5
\pages 632--645
\crossref{https://doi.org/10.1007/s10958-014-1953-5}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84940231934}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. M. Fomenko, “Lattice points in many-dimensional balls”, J. Math. Sci. (N. Y.), 225:6 (2017), 1012–1021  mathnet  crossref  mathscinet
    2. O. M. Fomenko, “O srednikh Rissa koeffitsientov dzeta-funktsii Epshteina”, Analiticheskaya teoriya chisel i teoriya funktsii. 33, Posvyaschaetsya pamyati Galiny Vasilevny KUZMINOI, Zap. nauchn. sem. POMI, 458, POMI, SPb., 2017, 218–235  mathnet
  • Записки научных семинаров ПОМИ
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