Geodesic
On the distribution of fractional parts of polynomials
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 26, Tome 392 (2011), pp. 191-201 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper upper bounds for sums of the form $$ \sum_{0<n\le N}\psi\big(f(n)\big), $$ where $f(x)$ is a polynomial and $\psi(x)=x-[x]-1/2$, are obtained. The cases $$ f(x)=\frac1\alpha x^2+\beta x+\gamma $$ and $$ f(x)=\frac1\alpha x^3+\beta x^2+\gamma x+\delta $$ are considered, where $\alpha$ is a large positive number. Weyl's method and V. N. Popov's reasoning (Mat. Zametki, 18 (1975), 699–704) are used. 
@article{ZNSL_2011_392_a9,
     author = {O. M. Fomenko},
     title = {On the distribution of fractional parts of polynomials},
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     year = {2011},
     volume = {392},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a9/}
}
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O. M. Fomenko. On the distribution of fractional parts of polynomials. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 26, Tome 392 (2011), pp. 191-201. http://geodesic.mathdoc.fr/item/ZNSL_2011_392_a9/

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