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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 6, Pages 1187–1226 (Mi izv1963)  

This article is cited in 4 scientific papers (total in 4 papers)

A sharp estimate for the number of solutions of a system of Diophantine equations

G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov


Abstract: A sharp estimate is obtained for the average of $|\Gamma|^{2k}$, where $\Gamma$ is an $r$-fold Weyl sum, valid for suitably large $k$.
Bibliography: 9 titles.

Full text: PDF file (3124 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:3, 461–497

Bibliographic databases:

UDC: 511
MSC: 10B15, 10G10
Received: 12.06.1978

Citation: G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “A sharp estimate for the number of solutions of a system of Diophantine equations”, Izv. Akad. Nauk SSSR Ser. Mat., 42:6 (1978), 1187–1226; Math. USSR-Izv., 13:3 (1979), 461–497

Citation in format AMSBIB
\Bibitem{ArkKarChu78}
\by G.~I.~Arkhipov, A.~A.~Karatsuba, V.~N.~Chubarikov
\paper A~sharp estimate for the number of solutions of a~system of Diophantine equations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 6
\pages 1187--1226
\mathnet{http://mi.mathnet.ru/izv1963}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=522938}
\zmath{https://zbmath.org/?q=an:0427.10011|0402.10016}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 3
\pages 461--497
\crossref{https://doi.org/10.1070/IM1979v013n03ABEH002075}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JG49100001}


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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, “Trigonometric integrals”, Math. USSR-Izv., 15:2 (1980), 211–239  mathnet  crossref  mathscinet  zmath  adsnasa  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. A. Zrein, “On the generalized Hua problem”, Izv. Math., 59:6 (1995), 1149–1171  mathnet  crossref  mathscinet  zmath  isi
    4. V. N. Chubarikov, “Mnogomernye problemy teorii prostykh chisel”, Chebyshevskii sb., 12:4 (2011), 174–263  mathnet  mathscinet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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