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Series and integrals of I. M. Vinogradov and their applications. (Russian) Zbl 0707.11059
In an earlier paper [Dokl. Akad. Nauk SSSR 300, No.4, 803-807 (1988; Zbl 0659.10043)], the author defined the “Vinogradov series” as generalizations of the Fourier series of a periodic function, and surveyed their properties and applications. Here a more detailed account is given. Also, “Vinogradov integrals” are discussed as continuous analogues of Vinogradov series.
Reviewer: M.Jutila

11L15 Weyl sums
42A99 Harmonic analysis in one variable
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