Geodesic
On the distribution of fractional parts of polynomials of two variables
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 222-232 
O. M. Fomenko. On the distribution of fractional parts of polynomials of two variables. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 27, Tome 404 (2012), pp. 222-232. http://geodesic.mathdoc.fr/item/ZNSL_2012_404_a13/
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     title = {On the distribution of fractional parts of polynomials of two variables},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

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