Geodesic
On an elementary version of I.M. Vinogradov's method
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 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. 
@article{TM_2017_296_a3,
     author = {V. N. Chubarikov},
     title = {On an elementary version of {I.M.} {Vinogradov's} method},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {47--57},
     publisher = {mathdoc},
     volume = {296},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2017_296_a3/}
}
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V. N. Chubarikov. On an elementary version of I.M. Vinogradov's method. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analytic and combinatorial number theory, Tome 296 (2017), pp. 47-57. http://geodesic.mathdoc.fr/item/TM_2017_296_a3/