Geodesic
Fractional Parts of the Function~$x/n$
Matematičeskie zametki, Tome 100 (2016) no. 5, pp. 744-756.

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Asymptotic formulas for sums of values of some class of smooth functions of fractional parts of numbers of the form $x/n$, where the parameter $x$ increases unboundedly and the integer $n$ ranges over various subsets of the interval $[1,x]$, are obtained.
Keywords: fractional parts, asymptotic behavior, divisor problem, method of trigonometric sums. 
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A. V. Shubin. Fractional Parts of the Function~$x/n$. Matematičeskie zametki, Tome 100 (2016) no. 5, pp. 744-756. http://geodesic.mathdoc.fr/item/MZM_2016_100_5_a9/

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