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Mat. Sb. (N.S.), 1977, Volume 103(145), Number 4(8), Pages 480–489 (Mi msb2921)  

This article is cited in 1 scientific paper (total in 1 paper)

Induced extremal surfaces

V. I. Bernik


Abstract: Under general assumptions on the functions $f_1(x),…,f_n(x)$ and $\varphi_1(y_1,…,y_k),…,\varphi_m(y_1,…,y_k)$ it is proved that the inequality
$$ \|a_1f_1+…+a_nf_n+a_{n+1}\varphi_1+…+a_{n+m}\varphi_m\|<H^{-(m+n)-\varepsilon}, $$
where $\|\alpha\|$ is the distance from $\alpha$ to the nearest integer and $H=\max|a_i|$, $i=1,…,n+m$, has only a finite number of solutions in integers $a_1,…,a_{n+m}$ for almost all $(x,y_1,…,y_k)\in R^{k+1}$. This establishes the extremality of the surface $(f_1,…,f_n,\varphi_1,…,\varphi_m)$.
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1977, 32:4, 413–421

Bibliographic databases:

UDC: 511
MSC: 10K15, 10B45, 14G99
Received: 25.05.1976

Citation: V. I. Bernik, “Induced extremal surfaces”, Mat. Sb. (N.S.), 103(145):4(8) (1977), 480–489; Math. USSR-Sb., 32:4 (1977), 413–421

Citation in format AMSBIB
\Bibitem{Ber77}
\by V.~I.~Bernik
\paper Induced extremal surfaces
\jour Mat. Sb. (N.S.)
\yr 1977
\vol 103(145)
\issue 4(8)
\pages 480--489
\mathnet{http://mi.mathnet.ru/msb2921}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=463133}
\zmath{https://zbmath.org/?q=an:0359.10042}
\transl
\jour Math. USSR-Sb.
\yr 1977
\vol 32
\issue 4
\pages 413--421
\crossref{https://doi.org/10.1070/SM1977v032n04ABEH002395}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1977GL81400002}


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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. V. G. Sprindzhuk, “Achievements and problems in Diophantine approximation theory”, Russian Math. Surveys, 35:4 (1980), 1–80  mathnet  crossref  mathscinet  zmath  adsnasa  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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