Geodesic
On the sum of the fractional parts $\sum_{n\leq x}\{ne\}$
Čebyševskij sbornik, Tome 11 (2010) no. 1, pp. 263-265.

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In the paper we prove unimproval in order of magnitude estimates for the remainder term in asymptotic formula for the sum $\sum_{n\le x} \{ne\}$. 
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A. V. Shutov. On the sum of the fractional parts $\sum_{n\leq x}\{ne\}$. Čebyševskij sbornik, Tome 11 (2010) no. 1, pp. 263-265. http://geodesic.mathdoc.fr/item/CHEB_2010_11_1_a27/

[1] Ilyasov I. I., Nugaeva Z. T., “Ob ostatke summy $\sum_{n\le x} \{ne\}$”, Algebra i teoriya chisel: sovremennye problemy i prilozheniya, Materialy VII mezhdunarodnoi konferentsii, posvyaschennoi pamyati professora Anatoliya Alekseevicha Karatsuby (Tula, 11–16 maya 2010 goda), TGPU, Tula, 2010, 93–94

[2] Brown T. C., Shiue P. J.-S., “Sums of Fractional Parts of Integer Multiplies of an Irrational”, Journal of Number Theory, 50 (1995), 181–192 | MR | Zbl