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

[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