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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 4, Pages 751–762 (Mi izv1789)  

This article is cited in 6 scientific papers (total in 7 papers)

A new estimate of an integral of I. M. Vinogradov

G. I. Arkhipov, A. A. Karatsuba


Abstract: A general theorem on estimating an integral of I. M. Vinogradov is proved, from which a number of consequences of independent interest are obtained.
Bibliography: 16 titles.

Full text: PDF file (947 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1979, 13:1, 52–62

Bibliographic databases:

Document Type: Article
UDC: 511
MSC: Primary 10G10; Secondary 10B15
Received: 09.03.1978

Citation: G. I. Arkhipov, A. A. Karatsuba, “A new estimate of an integral of I. M. Vinogradov”, Izv. Akad. Nauk SSSR Ser. Mat., 42:4 (1978), 751–762; Math. USSR-Izv., 13:1 (1979), 52–62

Citation in format AMSBIB
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\by G.~I.~Arkhipov, A.~A.~Karatsuba
\paper A~new estimate of an integral of I.\,M.~Vinogradov
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\yr 1978
\vol 42
\issue 4
\pages 751--762
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\zmath{https://zbmath.org/?q=an:0417.10013|0384.10009}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 1
\pages 52--62
\crossref{https://doi.org/10.1070/IM1979v013n01ABEH002010}
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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, 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
    2. G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Multiple trigonometric sums and their applications”, Math. USSR-Izv., 17:1 (1981), 1–54  mathnet  crossref  mathscinet  zmath  isi
    3. O. V. Tyrina, “A new estimate for a trigonometric integral of I. M. Vinogradov”, Math. USSR-Izv., 30:2 (1988), 337–351  mathnet  crossref  mathscinet  zmath
    4. A. A. Karatsuba, “The distribution of prime numbers”, Russian Math. Surveys, 45:5 (1990), 99–171  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. G. I. Arkhipov, V. I. Blagodatskikh, V. S. Vladimirov, S. M. Voronin, O. B. Lupanov, E. F. Mishchenko, Yu. V. Prokhorov, V. N. Chubarikov, A. B. Shidlovskii, “Anatolii Alekseevich Karatsuba (on his 60th birthday)”, Russian Math. Surveys, 53:2 (1998), 419–422  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. S. N. Preobrazhenskii, “New Estimate in Vinogradov's Mean-Value Theorem”, Math. Notes, 89:2 (2011), 277–290  mathnet  crossref  crossref  mathscinet  isi
    7. Kevin Ford, T.D.. Wooley, “On Vinogradov’s mean value theorem: strongly diagonal behaviour via efficient congruencing”, Acta Math, 213:2 (2014), 199  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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