On an elementary version of I.M. Vinogradov's method
Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 47-57.

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We prove estimates for complete rational arithmetic sums of Bernoulli polynomials whose arguments are formed by the fractional parts of values of a polynomial with rational coefficients. The results are applied to the problem of finding the convergence exponent for the mean values of the sums under consideration.
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V. N. Chubarikov. On an elementary version of I.M. Vinogradov's method. Informatics and Automation, Analytic and combinatorial number theory, Tome 296 (2017), pp. 47-57. http://geodesic.mathdoc.fr/item/TRSPY_2017_296_a3/

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