A~new estimate of an integral of I.\,M.~Vinogradov
Izvestiya. Mathematics , Tome 13 (1979) no. 1, pp. 52-62.

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A general theorem on estimating an integral of I. M. Vinogradov is proved, from which a number of consequences of independent interest are obtained. Bibliography: 16 titles.
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G. I. Arkhipov; A. A. Karatsuba. A~new estimate of an integral of I.\,M.~Vinogradov. Izvestiya. Mathematics , Tome 13 (1979) no. 1, pp. 52-62. http://geodesic.mathdoc.fr/item/IM2_1979_13_1_a2/

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

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

[3] Khua Lo-ken, Additivnaya teoriya prostykh chisel, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 22, 1947 | MR | Zbl

[4] Karatsuba A. A., “Problema Varinga dlya sravneniya po modulyu, ravnomu stepeni prostogo chisla”, Vestnik MGU, ser. 1, 1962, no. 1, 28–38 | Zbl

[5] Karatsuba A. A., “O sistemakh sravnenii”, Izv. AN SSSR. Ser. matem., 29 (1965), 935–944 | Zbl

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

[7] Karatsuba A. A., Metod trigonometricheskikh summ i teoremy o srednem, Doktorskaya dissertatsiya, M., 1966

[8] Karatsuba A. A., “Srednee znachenie modulya trigonometricheskoi summy”, Izv. AN SSSR. Ser. matem., 37 (1973), 1203–1227 | Zbl

[9] Karatsuba A. A., “Ob otsenke chisla reshenii nekotorykh uravnenii”, Dokl. AN SSSR, 165:1 (1965), 31–32 | Zbl

[10] Karatsuba A. A., “Sistemy sravnenii i uravneniya varingovskogo tipa”, Dokl. AN SSSR, 165:2 (1965), 274–276 | Zbl

[11] Linnik Yu. V., “Otsenki summ Veilya po metodu I. M. Vinogradova”, Izv. AN SSSR. Ser. matem., 6(1) (1942), 41–70 | MR | Zbl

[12] Linnik Yu. V., “Otsenki summ Veilya”, Dokl. AN SSSR, XXXIV:7 (1942), 201–203

[13] Linnik Yu. V., “O summakh Veilya”, Matem. sb., 12(57) (1942), 28–39 | MR

[14] Chandrasekkharan K., Arifmeticheskie funktsii, Nauka, M., 1975 | MR

[15] Stechkin S. B., “O srednikh znacheniyakh modulya trigonometricheskoi summy”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 134, 1975, 283–309 | Zbl

[16] Arkhipov G. I., Chubarikov V. N., “Kratnye trigonometricheskie summy”, Izv. AN SSSR. Ser. matem., 40 (1976), 209–220 | Zbl