Geodesic
On complete rational arithmetic sums of polynomial values
Informatics and Automation, Analytic number theory, Tome 299 (2017), pp. 56-61.

Voir la notice de l'article provenant de la source Math-Net.Ru

New estimates are obtained for complete arithmetic sums of polynomial values (exponential sums, sums of Dirichlet characters, and sums of Bernoulli polynomials) in the case where the derivative of the polynomial in the argument of the sum has no multiple roots modulo primes dividing the period of these arithmetic sums. 
@article{TRSPY_2017_299_a2,
     author = {V. N. Chubarikov},
     title = {On complete rational arithmetic sums of polynomial values},
     journal = {Informatics and Automation},
     pages = {56--61},
     publisher = {mathdoc},
     volume = {299},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2017_299_a2/}
}
TY  - JOUR
AU  - V. N. Chubarikov
TI  - On complete rational arithmetic sums of polynomial values
JO  - Informatics and Automation
PY  - 2017
SP  - 56
EP  - 61
VL  - 299
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2017_299_a2/
LA  - ru
ID  - TRSPY_2017_299_a2
ER  - 
%0 Journal Article
%A V. N. Chubarikov
%T On complete rational arithmetic sums of polynomial values
%J Informatics and Automation
%D 2017
%P 56-61
%V 299
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2017_299_a2/
%G ru
%F TRSPY_2017_299_a2
V. N. Chubarikov. On complete rational arithmetic sums of polynomial values. Informatics and Automation, Analytic number theory, Tome 299 (2017), pp. 56-61. http://geodesic.mathdoc.fr/item/TRSPY_2017_299_a2/

[1] G. I. Arkhipov, Selected Works, Orlovsk. Gos. Univ., Orel, 2013 (in Russian) | MR

[2] Arkhipov G.I., Chubarikov V.N., Karatsuba A.A., Trigonometric sums in number theory and analysis, de Gruyter Expo. Math., 39, W. de Gruyter, Berlin, 2004 | MR | Zbl

[3] V. N. Chubarikov, “Elementary derivation of an estimate for the complete rational arithmetic sum of a polynomial”, Chebyshev. Sb., 16:3 (2015), 450–459 | MR

[4] V. N. Chubarikov, “The rate of convergence of the average value of the complete rational arithmetic sums”, Chebyshev. Sb., 16:4 (2015), 303–318 | MR

[5] V. N. Chubarikov, “Arithmetic sums of polynomial values”, Dokl. Math., 93:1 (2016), 31–32 | DOI | MR | Zbl

[6] V. N. Chubarikov, “Complete rational arithmetic sums”, Moscow Univ. Math. Bull., 71 (2016), 43–44 | DOI | MR | Zbl

[7] Hua L.-K., Selected papers, Springer, New York, 1983 | MR | Zbl

[8] A. A. Karatsuba, Basic Analytic Number Theory, Springer, Berlin, 1993 | MR | MR | Zbl

[9] A. G. Postnikov, “On the sum of characters with respect to a modulus equal to a power of a prime number”, Izv. Akad. Nauk SSSR, Ser. Mat., 19:1 (1955), 11–16 | Zbl

[10] A. G. Postnikov, Selected Works, Fizmatlit, M., 2005 (in Russian) | MR

[11] D. O. Shklyarskii, G. M. Adel'son-Vel'skii, N. N. Chentsov, A. M. Yaglom, I. M. Yaglom, Selected Problems and Theorems in Elementary Mathematics, v. 1, Arithmetic and Algebra, Gostekhizdat, M., 1950 (in Russian)

[12] I. M. Vinogradov, The Method of Trigonometric Sums in Number Theory, 2nd ed., Nauka, M., 1980 (in Russian) | MR