Geodesic
Multiple trigonometric sums and their applications
Izvestiya. Mathematics , Tome 17 (1981) no. 1, pp. 1-54.

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The authors obtain results in the theory of multiple trigonometric sums that in essence take account of the domain of variation of the principal parameters. Bibliography: 6 titles. 
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G. I. Arkhipov; A. A. Karatsuba; V. N. Chubarikov. Multiple trigonometric sums and their applications. Izvestiya. Mathematics , Tome 17 (1981) no. 1, pp. 1-54. http://geodesic.mathdoc.fr/item/IM2_1981_17_1_a0/

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

[2] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., Kratnye trigonometricheskie summy, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 151, Nauka, M., 1980 | MR | Zbl

[3] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Tochnaya otsenka chisla reshenii odnoi sistemy diofantovykh uravnenii”, Izv. AN SSSR. Ser. matem., 42 (1978), 1187–1226 | MR | Zbl

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

[5] Arkhipov G. I., Karatsuba A. A., “Novaya otsenka integrala I. M. Vinogradova”, Izv. AN SSSR. Ser. matem., 42 (1978), 751–762 | MR | Zbl

[6] Karatsuba A. A., Osnovy analiticheskoi teorii chisel, Nauka, M., 1975 | MR | Zbl