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

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Matematicheskie Zametki, 1997, Volume 61, Issue 5, Pages 706–716
DOI: https://doi.org/10.4213/mzm1552 (Mi mzm1552)

This article is cited in 5 scientific papers (total in 6 papers)

On simultaneous Diophantine approximations. Vectors of given Diophantine type

N. G. Moshchevitin

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

Full-text PDF (1022 kB) Citations (6)

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

Abstract: For any monotone function

ψ (y) = O (y^{- 1 / s})

$\psi(y)=O(y^{-1/s})$ , we prove the existence of a continual family of vectors

$(\alpha_1,\dots,\alpha_s)\in\mathbb R^s$ admitting infinitely many simultaneous

$\psi$ -approximations, but no

$c\psi$ -approximations with some constant

$c>0$ .

Received: 01.06.1995

English version:
Mathematical Notes, 1997, Volume 61, Issue 5, Pages 590–599
DOI: https://doi.org/10.1007/BF02355080

Bibliographic databases:

UDC: 511.3

Language: Russian

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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\yr 1997

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\pages 706--716

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\transl

\jour Math. Notes

\yr 1997

\vol 61

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\pages 590--599

\crossref{https://doi.org/10.1007/BF02355080}

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Linking options:

https://www.mathnet.ru/eng/mzm1552

https://doi.org/10.4213/mzm1552

https://www.mathnet.ru/eng/mzm/v61/i5/p706

This publication is cited in the following 6 articles:

José Ventura‐León, Shirley Tocto‐Muñoz, Cristopher Lino‐Cruz, Andy Rick Sánchez‐Villena, Renzo Martinez‐Munive, Karim Talledo‐Sánchez, Kenia Casiano‐Valdivieso, “Myths of Romantic Love, Negative Interactions, Relationship Involvement, Satisfaction, Infidelity, and Jealousy in Peruvian Individuals With Couples: Directed and Undirected Network Analysis”, J Marital Family Therapy, 51:2 (2025)
Yu. A. Basalov, “O russkoi nauchnoi shkole diofantovykh priblizhenii”, Chebyshevskii sb., 21:1 (2020), 388–403
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
R. K. Akhunzhanov, N. G. Moshchevitin, “Vectors of Given Diophantine Type”, Math. Notes, 80:3 (2006), 318–328
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
N. G. Moshchevitin, “Best simultaneous approximations: norms, signatures, and asymptotic directions”, Math. Notes, 67:5 (2000), 618–624

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

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