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Mat. Zametki, 1977, Volume 21, Issue 6, Pages 799–806 (Mi mz8010)  

This article is cited in 2 scientific papers (total in 2 papers)

Integral points on strictly convex closed curves

S. V. Konyagin

M. V. Lomonosov Moscow State University

Abstract: A negative answer is given to Swinnerton–Dyer's question: Is it true that for any $\varepsilon>0$ there exists a positive integer $n$ such that for any planar closed strictly convex $n$-times differentiable curve $\Gamma$, when it is blown up a sufficiently large number $\nu$ of times, the number of integral points on the resultant curve will be less than $\nu^\varepsilon$. An example has been constructed when this number for an infinite number $\nu$ is not less than $\nu^{1/2}$, while $\Gamma$ is infinitely differentiable.

Full text: PDF file (398 kB)

English version:
Mathematical Notes, 1977, 21:6, 450–454

Bibliographic databases:

Document Type: Article
UDC: 511
Received: 08.04.1976

Citation: S. V. Konyagin, “Integral points on strictly convex closed curves”, Mat. Zametki, 21:6 (1977), 799–806; Math. Notes, 21:6 (1977), 450–454

Citation in format AMSBIB
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\by S.~V.~Konyagin
\paper Integral points on strictly convex closed curves
\jour Mat. Zametki
\yr 1977
\vol 21
\issue 6
\pages 799--806
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=460244}
\zmath{https://zbmath.org/?q=an:0399.10031|0355.10023}
\transl
\jour Math. Notes
\yr 1977
\vol 21
\issue 6
\pages 450--454
\crossref{https://doi.org/10.1007/BF01410173}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1977EJ13900019}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. N. Varchenko, “Number of lattice points in families of homothetic domains in $\mathbb{R}^n$”, Funct. Anal. Appl., 17:2 (1983), 79–83  mathnet  crossref  mathscinet  zmath  isi
    2. D. V. Kosygin, A. A. Minasov, Ya. G. Sinai, “Statistical properties of the spectra of Laplace–Beltrami operators on Liouville surfaces”, Russian Math. Surveys, 48:4 (1993), 1–142  mathnet  crossref  mathscinet  zmath  adsnasa  isi
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