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Matematicheskie Zametki, 2016, Volume 99, Issue 1, Pages 102–120
DOI: https://doi.org/10.4213/mzm10789 (Mi mzm10789) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Oscillation of the Measure of Irrationality Function in the Multidimensional Case

D. O. Shatskov

Astrakhan State University
Full-text PDF (573 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm10789
Abstract: It is proved that, for almost all pairs of $n\times m$ matrices $\Theta$, $\Theta'$, in the cases $m=1$ and $n=2$ or $m\ge2$ and $n=1$, the difference between the measure of irrationality functions $\psi_\Theta-\psi_{\Theta'}$ oscillates an infinite number of times as $t\to+\infty$.
Keywords: measure of irrationality function of a matrix, oscillation of a function, algebraically independent real numbers, Lebesgue measure, Borel–Cantelli sequence.
Funding agency Grant number
Russian Science Foundation 14-11-00433
This work was supported by the Russian Science Foundation under grant 14-11-00433.
Received: 29.01.2015
Revised: 21.06.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 1, Pages 120–137
DOI: https://doi.org/10.1134/S0001434616010132
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: D. O. Shatskov, “Oscillation of the Measure of Irrationality Function in the Multidimensional Case”, Mat. Zametki, 99:1 (2016), 102–120; Math. Notes, 99:1 (2016), 120–137
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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