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Zap. Nauchn. Sem. POMI, 2012, Volume 404, Pages 222–232 (Mi znsl5270)  

This article is cited in 1 scientific paper (total in 1 paper)

On the distribution of fractional parts of polynomials of two variables

O. M. Fomenko

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: In the paper, upper bounds for sums of the form
$$ \underset{(n_1,n_2)\in\Omega}{\sum\sum}\psi(f(n_1,n_2)), $$
where $\psi(x)=x-[x]-\frac12$, $f(x,y)$ is a polynomial, $(n_1,n_2)\in\mathbb Z^2$, and $\Omega$ is a domain in $\mathbb R^2$, are obtained.
One of the upper bounds is of interest, particularly in connection with a lattice point problem considered in Theorem 2.

Key words and phrases: fractional parts of polynomials, lattice point problem.

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English version:
Journal of Mathematical Sciences (New York), 2013, 193:1, 129–135

Bibliographic databases:

UDC: 511.466+517.863
Received: 25.05.2012

Citation: O. M. Fomenko, “On the distribution of fractional parts of polynomials of two variables”, Analytical theory of numbers and theory of functions. Part 27, Zap. Nauchn. Sem. POMI, 404, POMI, St. Petersburg, 2012, 222–232; J. Math. Sci. (N. Y.), 193:1 (2013), 129–135

Citation in format AMSBIB
\Bibitem{Fom12}
\by O.~M.~Fomenko
\paper On the distribution of fractional parts of polynomials of two variables
\inbook Analytical theory of numbers and theory of functions. Part~27
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 404
\pages 222--232
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5270}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3029603}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 193
\issue 1
\pages 129--135
\crossref{https://doi.org/10.1007/s10958-013-1441-3}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884976991}


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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 the circle and the sphere”, J. Math. Sci. (N. Y.), 200:5 (2014), 632–645  mathnet  crossref
  • Записки научных семинаров ПОМИ
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