Geodesic
Linear sums and the Gaussian multiplication theorem
Čebyševskij sbornik, Tome 17 (2016) no. 1, pp. 130-139

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

Estimations of linear sums with Bernoulli polynomial of the first degree are given. If the coefficient of the linear function is a irrational number with the bounded partial quotients, the arithmetical sum has the “squaring” estimation. The Roth's theorem gives the similar estimation for all algebraic number, but the constants in estimations be nonefficient. New difficulties appears for sums over primes. Their are connected with the consideration of bilinear forms. Bibliography: 24 titles.
Keywords: arithmetical sums, the Gaussian multiplication theorem for the Euler's Gamma-function, the functional theorem of the Gaussian type, the Bernoulli polynomials, algebraic numbers, arithmetical sums over primes, the Roth's theorem. 
@article{CHEB_2016_17_1_a9,
     author = {O. V. Kolpakova and V. N. Chubarikov},
     title = {Linear sums and the {Gaussian} multiplication theorem},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {130--139},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2016_17_1_a9/}
}
TY  - JOUR
AU  - O. V. Kolpakova
AU  - V. N. Chubarikov
TI  - Linear sums and the Gaussian multiplication theorem
JO  - Čebyševskij sbornik
PY  - 2016
SP  - 130
EP  - 139
VL  - 17
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHEB_2016_17_1_a9/
LA  - ru
ID  - CHEB_2016_17_1_a9
ER  - 
%0 Journal Article
%A O. V. Kolpakova
%A V. N. Chubarikov
%T Linear sums and the Gaussian multiplication theorem
%J Čebyševskij sbornik
%D 2016
%P 130-139
%V 17
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHEB_2016_17_1_a9/
%G ru
%F CHEB_2016_17_1_a9
O. V. Kolpakova; V. N. Chubarikov. Linear sums and the Gaussian multiplication theorem. Čebyševskij sbornik, Tome 17 (2016) no. 1, pp. 130-139. http://geodesic.mathdoc.fr/item/CHEB_2016_17_1_a9/