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Mat. Zametki, 1997, Volume 61, Issue 5, Pages 706–716 (Mi mz1552)  

This article is cited in 4 scientific papers (total in 5 papers)

On simultaneous Diophantine approximations. Vectors of given Diophantine type

N. G. Moshchevitin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: For any monotone function $\psi(y)=O(y^{-1/s})$, we prove the existence of a continual family of vectors $(\alpha_1,…,\alpha_s)\in\mathbb R^s$ admitting infinitely many simultaneous $\psi$-approximations, but no $c\psi$-approximations with some constant $c>0$.

DOI: https://doi.org/10.4213/mzm1552

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English version:
Mathematical Notes, 1997, 61:5, 590–599

Bibliographic databases:

UDC: 511.3
Received: 01.06.1995

Citation: N. G. Moshchevitin, “On simultaneous Diophantine approximations. Vectors of given Diophantine type”, Mat. Zametki, 61:5 (1997), 706–716; Math. Notes, 61:5 (1997), 590–599

Citation in format AMSBIB
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\by N.~G.~Moshchevitin
\paper On simultaneous Diophantine approximations. Vectors of given Diophantine type
\jour Mat. Zametki
\yr 1997
\vol 61
\issue 5
\pages 706--716
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\crossref{https://doi.org/10.4213/mzm1552}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1620125}
\zmath{https://zbmath.org/?q=an:0916.11040}
\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 5
\pages 590--599
\crossref{https://doi.org/10.1007/BF02355080}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997YE52200008}


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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. N. G. Moshchevitin, “Best simultaneous approximations: norms, signatures, and asymptotic directions”, Math. Notes, 67:5 (2000), 618–624  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. V. Rozhdestvenskii, “On the additive cohomological equation and time change for a linear flow on the torus with a Diophantine frequency vector”, Sb. Math., 195:5 (2004), 723–764  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. R. K. Akhunzhanov, N. G. Moshchevitin, “Vectors of Given Diophantine Type”, Math. Notes, 80:3 (2006), 318–328  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Moshchevitin N.G., “Proof of W. M. Schmidt's Conjecture Concerning Successive Minima of a Lattice”, J. Lond. Math. Soc.-Second Ser., 86:Part 1 (2012), 129–151  crossref  mathscinet  zmath  isi  scopus  scopus
    5. Yu. A. Basalov, “O russkoi nauchnoi shkole diofantovykh priblizhenii”, Chebyshevskii sb., 21:1 (2020), 388–403  mathnet  crossref
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