Geodesic
Multiple trigonometric sums
Izvestiya. Mathematics, Tome 10 (1976) no. 1, pp. 200-210 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove a multidimensional analog of I. M. Vinogradov's theorem on the mean value of the modulus of a trigonometric sum. We illustrate the possibility of using our theorem to estimate multiple trigonometric sums with the example of the simplest type of multiple trigonometric sums. Bibliography: 9 titles. 
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G. I. Arkhipov; V. N. Chubarikov. Multiple trigonometric sums. Izvestiya. Mathematics, Tome 10 (1976) no. 1, pp. 200-210. http://geodesic.mathdoc.fr/item/IM2_1976_10_1_a10/

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

[3] Karatsuba A. A., “Problema Varinga dlya sravneniya po modulyu, ravnomu stepeni prostogo chisla”, Vestnik MGU, 1 (1962), 28–38

[4] Linnik Yu. V., “Novye otsenki summ Veilya”, Dokl. AN SSSR, 34:7 (1942), 201–203 | MR

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

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

[8] Arkhipov G. I., “Kratnye trigonometricheskie summy”, Dokl. AN SSSR, 219:5 (1974), 1036–1037 | Zbl

[9] Arkhipov G. I., “Teorema o srednem znachenii modulya kratnoi trigonometricheskoi summy”, Matem. zametki, 17:1 (1975), 143–153 | MR | Zbl