Geodesic
The arithmetic sum and Gaussian multiplication theorem
Čebyševskij sbornik, Tome 16 (2015) no. 2, pp. 231-253

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

The paper presents the fundamentals of the theory of arithmetic sums  and oscillatory integrals of polynomials Bernoulli, an argument that is the real function of a certain differential properties. Drawing an analogy with the method of trigonometric sums I. M. Vinogradov. The introduction listed problems in number theory and mathematical analysis, which deal the study of the above mentioned sums and integrals. Research arithmetic sums essentially uses a functional equation type Gauss theorem for multiplication of the Euler gamma function. Estimations of the individual arithmetic the amounts found indicators of convergence of their averages. In particular, the problems are solved analogues Hua Loo-Keng for one-dimensional integrals and sums. Bibliography: 21 titles.
Keywords: arithmetic sum oscillatory integrals, polynomials Bernoulli, Gauss theorem for multiplication of the Euler gamma function, functional equation, the average values of the convergence exponent arithmetic sums and oscillatory integrals, Vinogradov's method of trigonometric sums, problems Hua Loo-Keng. 
@article{CHEB_2015_16_2_a14,
     author = {V. N. Chubarikov},
     title = {The arithmetic sum and {Gaussian} multiplication theorem},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {231--253},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2015_16_2_a14/}
}
TY  - JOUR
AU  - V. N. Chubarikov
TI  - The arithmetic sum and Gaussian multiplication theorem
JO  - Čebyševskij sbornik
PY  - 2015
SP  - 231
EP  - 253
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2015_16_2_a14/
LA  - ru
ID  - CHEB_2015_16_2_a14
ER  - 
%0 Journal Article
%A V. N. Chubarikov
%T The arithmetic sum and Gaussian multiplication theorem
%J Čebyševskij sbornik
%D 2015
%P 231-253
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2015_16_2_a14/
%G ru
%F CHEB_2015_16_2_a14
V. N. Chubarikov. The arithmetic sum and Gaussian multiplication theorem. Čebyševskij sbornik, Tome 16 (2015) no. 2, pp. 231-253. http://geodesic.mathdoc.fr/item/CHEB_2015_16_2_a14/