Geodesic
Estimates of the Averaged Sums of Fractional Parts
Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 298-308

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We establish asymptotically sharp estimates for the sums of the inverses (and more general sums) of the fractional parts $\{i\theta\}$ of irrational numbers $\theta$, depending on the arithmetical characteristics of the numbers $\theta$.
Keywords: averaged sum of fractional parts, irrational number, continued fraction, monotone function, Khinchin's theorem.
Mots-clés : convergent, Abel transformation 
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     author = {E. A. Sevast'yanov and I. Yu. Yakupov},
     title = {Estimates of the {Averaged} {Sums} of {Fractional} {Parts}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {298--308},
     publisher = {mathdoc},
     volume = {99},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_2_a12/}
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E. A. Sevast'yanov; I. Yu. Yakupov. Estimates of the Averaged Sums of Fractional Parts. Matematičeskie zametki, Tome 99 (2016) no. 2, pp. 298-308. http://geodesic.mathdoc.fr/item/MZM_2016_99_2_a12/