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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 1, Pages 209–220 (Mi izv2106)  

This article is cited in 9 scientific papers (total in 9 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.

Full text: PDF file (811 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:1, 200–210

Bibliographic databases:

UDC: 517.5
MSC: Primary 10G05; Secondary 10B15, 10B45
Received: 25.02.1975

Citation: G. I. Arkhipov, V. N. Chubarikov, “Multiple trigonometric sums”, Izv. Akad. Nauk SSSR Ser. Mat., 40:1 (1976), 209–220; Math. USSR-Izv., 10:1 (1976), 200–210

Citation in format AMSBIB
\Bibitem{ArkChu76}
\by G.~I.~Arkhipov, V.~N.~Chubarikov
\paper Multiple trigonometric sums
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 1
\pages 209--220
\mathnet{http://mi.mathnet.ru/izv2106}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=419376}
\zmath{https://zbmath.org/?q=an:0324.10038}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 1
\pages 200--210
\crossref{https://doi.org/10.1070/IM1976v010n01ABEH001685}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. I. Arkhipov, A. A. Karatsuba, “A new estimate of an integral of I. M. Vinogradov”, Math. USSR-Izv., 13:1 (1979), 52–62  mathnet  crossref  mathscinet  zmath  isi
    2. 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  mathnet  crossref  mathscinet  zmath  isi
    3. V. N. Chubarikov, “Kratnye trigonometricheskie summy”, Chebyshevskii sb., 12:4 (2011), 134–173  mathnet  mathscinet
    4. V. N. Chubarikov, “Mnogomernye problemy teorii prostykh chisel”, Chebyshevskii sb., 12:4 (2011), 174–263  mathnet  mathscinet
    5. V. N. Chubarikov, “Arifmeticheskie summy i gaussova teorema umnozheniya”, Chebyshevskii sb., 16:2 (2015), 231–253  mathnet  elib
    6. V. N. Chubarikov, “Pokazatel skhodimosti srednego znacheniya polnykh ratsionalnykh arifmeticheskikh summ”, Chebyshevskii sb., 16:4 (2015), 303–318  mathnet  elib
    7. V. N. Chubarikov, “A certain mean value theorem in the number theory”, Moscow University Mathematics Bulletin, 70:5 (2015), 230–233  mathnet  crossref  mathscinet
    8. O. V. Kolpakova, V. N. Chubarikov, “Lineinye summy i gaussova teorema umnozheniya”, Chebyshevskii sb., 17:1 (2016), 130–139  mathnet  elib
    9. V. N. Chubarikov, “On an elementary version of I.M. Vinogradov's method”, Proc. Steklov Inst. Math., 296 (2017), 41–51  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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