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A metrical result on the approximation by continued fractions

Author: H. Jager
Journal: Math. Comp. 81 (2012), 2377-2382
MSC (2010): Primary 11K50
Published electronically: May 22, 2012
MathSciNet review: 2945161
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Abstract: Let $ x$ be a real irrational number and $ p_n/q_n, \,\,n=0,1,2,\ldots $ its sequence of continued fraction convergents. Define $ \theta _n=q_n\big \vert q_nx-p_n\big \vert.$ For almost all $ x$ the distribution function of the sequence $ \big \vert\theta _{n+1}-\theta _{n-1}\big \vert, \,\,n=0,1,2,\ldots $ is determined and its expectation calculated.

References [Enhancements On Off] (What's this?)

  • 1. KarmaDajani and CorKraaikamp, Ergodic Theory of Numbers, The Mathematical Association of America, The Carus Mathematical Monographs 29, (2002). MR 1917322 (2003f:37014)
  • 2. J. F. Koksma, Diophantische Approximationen, Verlag Julius Springer, Berlin 1937. MR 0344200 (49:8940)
  • 3. H.Jager, The distribution of certain sequences connected with the continued fraction, Indag. Math. Series A 89, 1986, 61-69. MR 834320 (87g:11092)

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Additional Information

H. Jager
Affiliation: Oude Larenseweg 26, 7214 PC Epse, the Netherlands

Keywords: Continued fractions, approximation coefficients, metrical theory
Received by editor(s): May 19, 2011
Published electronically: May 22, 2012
Article copyright: © Copyright 2012 American Mathematical Society

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