Geodesic
The mean value of the modulus of a~trigonometric sum
Izvestiya. Mathematics , Tome 7 (1973) no. 6, pp. 1199-1223.

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

We obtain a simplified upper bound which is uniform in all parameters for the mean value of the modulus of a trigonometric sum. 
@article{IM2_1973_7_6_a0,
     author = {A. A. Karatsuba},
     title = {The mean value of the modulus of a~trigonometric sum},
     journal = {Izvestiya. Mathematics },
     pages = {1199--1223},
     publisher = {mathdoc},
     volume = {7},
     number = {6},
     year = {1973},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a0/}
}
TY  - JOUR
AU  - A. A. Karatsuba
TI  - The mean value of the modulus of a~trigonometric sum
JO  - Izvestiya. Mathematics 
PY  - 1973
SP  - 1199
EP  - 1223
VL  - 7
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a0/
LA  - en
ID  - IM2_1973_7_6_a0
ER  - 
%0 Journal Article
%A A. A. Karatsuba
%T The mean value of the modulus of a~trigonometric sum
%J Izvestiya. Mathematics 
%D 1973
%P 1199-1223
%V 7
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a0/
%G en
%F IM2_1973_7_6_a0
A. A. Karatsuba. The mean value of the modulus of a~trigonometric sum. Izvestiya. Mathematics , Tome 7 (1973) no. 6, pp. 1199-1223. http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a0/

[1] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1971 | MR

[2] Karatsuba A. A., “Ob odnoi sisteme neopredelennykh uravnenii”, Matem. zametki, 4:2 (1968), 125–128 | Zbl

[3] Karatsuba A. A., “Teoremy o srednem i polnye trigonometricheskie summy”, Izv. AN SSSR. Ser. matem., 30 (1966), 183–206 | Zbl

[4] Linnik Yu. V., “Novye otsenki summ Veilya”, Dokl. AN SSSR, 37:7 (1942), 201–203 | MR

[5] Chandrasekharan K., Arithinetical functions, Springen-Verlag, Berlin, 1970 | MR | Zbl