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

Mathematics of the USSR-Izvestiya

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Forthcoming papers
	Archive
	Impact factor
	Guidelines for authors
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Mathematics of the USSR-Izvestiya, 1979, Volume 13, Issue 3, Pages 461–497
DOI: https://doi.org/10.1070/IM1979v013n03ABEH002075 (Mi im1963)

This article is cited in 5 scientific papers (total in 5 papers)

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

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

English version PDF (1411 kB) Citations (5) Russian version article

References:

PDF

HTML

DOI: https://doi.org/10.1070/IM1979v013n03ABEH002075

Abstract: A sharp estimate is obtained for the average of

| Γ |^{2 k}

$|\Gamma|^{2k}$ , where

Γ

$\Gamma$ is an

r

$r$ -fold Weyl sum, valid for suitably large

k

$k$ .
Bibliography: 9 titles.

Received: 12.06.1978

Bibliographic databases:

Document Type: Article

UDC: 511

MSC: 10B15, 10G10

Language: English

Original paper language: Russian

Citation: 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

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 Math. USSR-Izv.

\yr 1979

\vol 13

\issue 3

\pages 461--497

\mathnet{http://mi.mathnet.ru/eng/im1963}

\crossref{https://doi.org/10.1070/IM1979v013n03ABEH002075}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=522938}

\zmath{https://zbmath.org/?q=an:0427.10011|0402.10016}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1979JG49100001}

Linking options:

https://www.mathnet.ru/eng/im1963

https://doi.org/10.1070/IM1979v013n03ABEH002075

https://www.mathnet.ru/eng/im/v42/i6/p1187

This publication is cited in the following 5 articles:

M. A. Korolev, “The estimate of weighted Kloosterman sums by additive shift”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 221–229
V. N. Chubarikov, “Mnogomernye problemy teorii prostykh chisel”, Chebyshevskii sb., 12:4 (2011), 174–263
A. Zrein, “On the generalized Hua problem”, Izv. Math., 59:6 (1995), 1149–1171
G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Multiple trigonometric sums and their applications”, Math. USSR-Izv., 17:1 (1981), 1–54
G. I. Arkhipov, A. A. Karatsuba, V. N. Chubarikov, “Trigonometric integrals”, Math. USSR-Izv., 15:2 (1980), 211–239

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

Известия Академии наук СССР. Серия математическая

Statistics & downloads:
Abstract page:	600
Russian version PDF:	221
English version PDF:	29
References:	83
First page:	4

Что такое QR-код?

Registration to the website

Logotypes