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Matematicheskie Zametki, 2015, Volume 98, Issue 2, Pages 271–287
DOI: https://doi.org/10.4213/mzm9374 (Mi mzm9374) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the Mean Value of the Measure of Irrationality of Real Numbers

D. O. Shatskov

Astrakhan State University
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DOI: https://doi.org/10.4213/mzm9374
Abstract: This paper deals with the asymptotic behavior of the integral
$$ I_\alpha(t)=\int_1^t \psi_\alpha(\xi)\,d\xi, \qquad\text{where}\quad \psi_\alpha(t)=\min_{1\le q\le t}\|q\alpha\| $$
(here the minimum is taken over integers $q$ and $\|\,\cdot\,\|$ denotes the distance to the nearest integer).
Keywords: real number, measure of irrationality, continued fraction, convergent, Lebesgue measure, Gauss transformation, ergodic transformation.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-05700
This work was supported by the Russian Foundation for Basic Research (grant no. 15-01-05700).
Received: 07.04.2012
Revised: 01.03.2015
English version:
Mathematical Notes, 2015, Volume 98, Issue 2, Pages 301–315
DOI: https://doi.org/10.1134/S0001434615070329
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: D. O. Shatskov, “On the Mean Value of the Measure of Irrationality of Real Numbers”, Mat. Zametki, 98:2 (2015), 271–287; Math. Notes, 98:2 (2015), 301–315
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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