Geodesic
Elementary of the complete rational arithmetical sums
Čebyševskij sbornik, Tome 16 (2015) no. 3, pp. 450-459

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In the paper the estimate of the complete rational arithmetical sum from a polynomial is found. It's is a correct on the power of a denominator with the estimate of the constant depending of the degree of a polynomial. Bibliography: 10 titles.
Keywords: the Gauss theorem of a multiplication for the Euler gamma-function, complete rational arithmetical sums, a functional equation on a complete system of residues by modulo of natural number, the Bernulli polynomials. 
V. N. Chubarikov. Elementary of the complete rational arithmetical sums. Čebyševskij sbornik, Tome 16 (2015) no. 3, pp. 450-459. http://geodesic.mathdoc.fr/item/CHEB_2015_16_3_a21/
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[1] Vinogradov I. M., The method of trigonometric sums in the theory of numbers, 2nd edition, Nauka, M., 1980, 144 pp. (in Russian)

[2] Chen Jing-run, “On Professor Hua's estimate on exponential sum”, Acta Sci. Sinica, 20:6 (1977), 711–719 | MR | Zbl

[3] Arkhipov G. I., Selected works, Orl. Gos. Univ., Orel, 2013, 464 pp. (in Russian)

[4] Arkhipov G. I., Chubarikov V. N., Karatsuba A. A., Trigonometric Sums in Number Theory and Analysis, De Gruyter expositions in mathematics, 39, Berlin–New York, 2004, 554 pp. | MR | Zbl

[5] Romanov N. P., Number theory and functional analysis, Collected papers, Tom. Univ., Tomsk, 2013, 478 pp. (in Russian)