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Fractional parts of the function x/n

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Abstract

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.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Moscow Oblast, Russia

    A. V. Shubin

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  1. A. V. Shubin
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Correspondence to A. V. Shubin.

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Original Russian Text © A. V. Shubin, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 5, pp. 744–756.

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Shubin, A.V. Fractional parts of the function x/n . Math Notes 100, 731–742 (2016). https://doi.org/10.1134/S0001434616110109

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  • DOI: https://doi.org/10.1134/S0001434616110109

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