This article is cited in 10 papers

Multiple trigonometric sums

G. I. Arkhipov, V. N. Chubarikov


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.

UDC: 517.5

MSC: Primary 10G05; Secondary 10B15, 10B45

Received: 25.02.1975

 English version: Mathematics of the USSR-Izvestiya, 1976, 10:1, 200–210

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