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A Gauss-Kusmin Theorem for Optimal Continued Fractions  (Make Corrections)  
Karma Dajani and Cor Kraaikamp



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Abstract: this paper is to obtain a Gauss-Kusmin theorem for the OCF. To be more precise, we will show \Gamma among many other things \Gamma that for z 2 [\Gamma ; g] () f 2 [\Gamma 1 2 zg = ([\Gamma 1 ; g) with density d (x), given by (x) = ? ? ? ? ? ? ! ? ? ? ? ? ? 2x+1 2x 2 +2x+1 if \Gamma 2 x ! \Gammag log G x+1 +2x+2 if \Gamma g x ! 3 1\Gammax\Gammax (x +2x+2)(2x \Gamma2x+1) if 2 x ! g; (8) and where T is given by = [ 0; " n+1 b n+1 ; " n+2 b... (Update)

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BibTeX entry:   (Update)

@misc{ and-gausskusmin,
  author = "Karma Dajani And",
  title = "A Gauss-Kusmin Theorem for Optimal Continued Fractions",
  url = "citeseer.ist.psu.edu/562617.html" }
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2   Kraaikamp -- Generalization of a Theorem by Kusmin (context) - Dajani - 1994
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2   Eine Bemerkung zu den verschiedenen Moglichkeiten eine Zahl .. (context) - Keller - 1939
2   Kraaikamp -- Metrical Theory for Optimal Continued Fractions (context) - Bosma - 1990
2   The Distribution of Continued Fraction Approximations (context) - Knuth - 1984
2   Kraaikamp -- Optimal approximation by optimal continued frac.. (context) - Bosma - 1991
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2   Uber die mittlere Schrittanzahl bei Divisionsalgorithmen (context) - Rieger - 1978
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1   Sur le loi de probabilit'e dont dependent les quotients comp.. (context) - L'evy - 1929
1   A very simple proof of a generalization of the Gauss-Kuzmin-.. (context) - Iosifescu
1   Metrische Theorie einer Klasse zahlentheoretischer Transform.. (context) - Schweiger

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