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Mat. Zametki, 2015, Volume 98, Issue 2, Pages 271–287 (Mi mz9374)  

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

Abstract: This paper deals with the asymptotic behavior of the integral
$$ I_\alpha(t)=\int_1^t \psi_\alpha(\xi) d\xi, \qquadwhere\quad \psi_\alpha(t)=\min_{1\le q\le t}\|q\alpha\| $$
(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).


DOI: https://doi.org/10.4213/mzm9374

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English version:
Mathematical Notes, 2015, 98:2, 301–315

Bibliographic databases:

UDC: 517
Received: 07.04.2012
Revised: 01.03.2015

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Moshchevitin N., “Uber Die Funktionen Des Irrationalitatsma Ss Es fur Zwei Irrationale Zahlen”, Arch. Math., 112:2 (2019), 161–168  crossref  mathscinet  zmath  isi  scopus
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