Abstract:
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.
This publication is cited in the following 10 articles:
V. N. Chubarikov, “On an elementary version of I.M. Vinogradov's method”, Proc. Steklov Inst. Math., 296 (2017), 41–51
O. V. Kolpakova, V. N. Chubarikov, “Lineinye summy i gaussova teorema umnozheniya”, Chebyshevskii sb., 17:1 (2016), 130–139
V. N. Chubarikov, “Arithmetic sums of polynomial values”, Dokl. Math., 93:1 (2016), 31
V. N. Chubarikov, “Arifmeticheskie summy i gaussova teorema umnozheniya”, Chebyshevskii sb., 16:2 (2015), 231–253
V. N. Chubarikov, “Pokazatel skhodimosti srednego znacheniya polnykh ratsionalnykh arifmeticheskikh summ”, Chebyshevskii sb., 16:4 (2015), 303–318
V. N. Chubarikov, “A certain mean value theorem in the number theory”, Moscow University Mathematics Bulletin, 70:5 (2015), 230–233
V. N. Chubarikov, “Kratnye trigonometricheskie summy”, Chebyshevskii sb., 12:4 (2011), 134–173
V. N. Chubarikov, “Mnogomernye problemy teorii prostykh chisel”, Chebyshevskii sb., 12:4 (2011), 174–263
G. I. Arkhipov, A. A. Karatsuba, “A new estimate of an integral of I. M. Vinogradov”, Math. USSR-Izv., 13:1 (1979), 52–62
G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “A sharp estimate for the number of solutions of a system of Diophantine equations”, Math. USSR-Izv., 13:3 (1979), 461–497
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