Geodesic
Estimates of multiple trigonometric sums with prime numbers
Izvestiya. Mathematics , Tome 27 (1986) no. 2, pp. 323-357.

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The author obtains estimates for multiple trigonometric sums with a general polynomial in the exponent whose variables of summation take the values of the successive prime numbers. The precision of the estimates is similar to that of the estimates in the paper "Multiple trigonometric sums and their applications" by Arkhipov, Karatsuba and Chubarikov (Izv. Akad. Nauk SSSR Ser. Mat., 1980, v. 44, № 4, p. 723–781). Bibliography: 12 titles. 
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     title = {Estimates of multiple trigonometric sums with prime numbers},
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V. N. Chubarikov. Estimates of multiple trigonometric sums with prime numbers. Izvestiya. Mathematics , Tome 27 (1986) no. 2, pp. 323-357. http://geodesic.mathdoc.fr/item/IM2_1986_27_2_a6/

[1] Vinogradov I. M., Izbrannye trudy, AN SSSR, M., 1952 | MR | Zbl

[2] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1980 | MR

[3] Karatsuba A. A., Osnovy analiticheskoi teorii chisel, Nauka, M., 1983 | MR

[4] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Kratnye trigonometricheskie summy”, Trudy Matem. in-ta im. V. A. Steklova AN SSSR, 151, 1980, 1–128 | MR | Zbl

[5] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Kratnye trigonometricheskie summy i ikh prilozheniya”, Izv. AN SSSR. Ser. matem., 44:4 (1980), 723–781 | MR | Zbl

[6] Arkhipov G. I., Karatsuba A. A., Chubarikov V. N., “Osobye sluchai teorii kratnykh trigonometricheskikh summ”, Izv. AN SSSR. Ser. matem., 47:4 (1983), 707–784 | MR | Zbl

[7] Vinogradov I. M., “O nekotorykh novykh problemakh teorii chisel”, Dokl. AN SSSR, 3:1 (1934), 1–6 | MR | Zbl

[8] Mardzhanishvili K. K., “Ob odnoi zadache additivnoi teorii chisel”, Izv. AN SSSR. Ser. matem., 4:2 (1940), 193–214 | Zbl

[9] Arkhipov G. I., “O probleme Gilberta–Kamke”, Izv. AN SSSR. Ser. matem., 48:1 (1984), 3–52 | MR | Zbl

[10] Khua Lo-gen, “Additivnaya teoriya prostykh chisel”, Trudy Matem. in-ta im. V. A. Steklova AN SSSR, 22, 1947, 3–179 | MR | Zbl

[11] Arkhipov G. I., Chubarikov V. N., “Ob arifmeticheskikh usloviyakh razreshimosti nelineinykh sistem diofantovykh uravnenii”, Dokl. AN SSSR, 284:1 (1985), 16–21 | MR

[12] Chubarikov V. N., “Kratnye trigonometricheskie summy s prostymi chislami”, Dokl. AN SSSR, 278:2 (1984), 302–304 | MR | Zbl