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Zap. Nauchn. Sem. POMI, 2016, Volume 449, Pages 261–274 (Mi znsl6331)  

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

Lattice points in many-dimensional balls

O. M. Fomenko

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

Abstract: Let $P_k(n)$ be the difference of the number of points of the integer lattice contained in the ball $y_1^2+…+y_k^2\leq n$ and the volume of this ball. We investigate the asymptotic behavior of the sums $\sum_{n\leq x}P_k(n)$, $(k\geq4)$, $\sum_{n\leq x}P_3^2(n)$, and $\sum_{n\leq x}P_4^2(n)$ as $x\to+\infty$.

Key words and phrases: many-dimensional balls, integral mean values, discrete mean values.

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English version:
Journal of Mathematical Sciences (New York), 2017, 225:6, 1012–1021

Bibliographic databases:

Document Type: Article
UDC: 511.466+517.863
Received: 17.10.2016

Citation: O. M. Fomenko, “Lattice points in many-dimensional balls”, Analytical theory of numbers and theory of functions. Part 32, Zap. Nauchn. Sem. POMI, 449, POMI, St. Petersburg, 2016, 261–274; J. Math. Sci. (N. Y.), 225:6 (2017), 1012–1021

Citation in format AMSBIB
\Bibitem{Fom16}
\by O.~M.~Fomenko
\paper Lattice points in many-dimensional balls
\inbook Analytical theory of numbers and theory of functions. Part~32
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 449
\pages 261--274
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6331}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3580140}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 225
\issue 6
\pages 1012--1021
\crossref{https://doi.org/10.1007/s10958-017-3512-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85027367940}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. O. M. Fomenko, “Tselye tochki v chetyrekhmernom share”, Analiticheskaya teoriya chisel i teoriya funktsii. 33, Posvyaschaetsya pamyati Galiny Vasilevny KUZMINOI, Zap. nauchn. sem. POMI, 458, POMI, SPb., 2017, 236–246  mathnet
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