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Some metrical observations on the approximation of an irrational number by its nearest mediants

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  1. [1]

    P. Billingsley,Ergodic Theory and Information, John Wiley and Sons, New York, London, Sydney, 1965MR 33:254

  2. [2]

    W. Bosma, H. Jager, andF. Wiedijk, Some metrical observations on the approximation by continued fractions,Proc. Kon. Ned. Akad. van Wetensch.,A86, (1983), 281–299.

  3. [3]

    P. Erdős, Some results on Diophantine approximation,Acta Arithmetica,5 (1959), 359–369.

  4. [4]

    P. Fatou, Sur l'approximation des incommensurables et les series trigonométriques,C. R. Acad. Sci., Paris,139, (1904), 1019–1021.

  5. [5]

    Sh. Ito, Algorithms with mediant convergents and their metrical theory, Preprint.

  6. [6]

    Sh. Ito, andH. Nakada, On natural extensions of transformations related to Diophantine approximations,Proceedings of the Conference on Number Theory and Combinatorics, World Scientific Publ. Co., Singapore.

  7. [7]

    H. Jager, The distribution of certain sequences connected with the continued fraction,Proc. Kon. Ned. Akad. van Wetensch.,A89 (1986), 61–69.

  8. [8]

    H. Jager, Continued Fractions and Ergodic Theory,Transcendental Numbers and Related Topics, RIMS Kokyuroku599, Kyoto University, Kyoto, Japan, (1986), 55–59.

  9. [9]

    J. F. Koksma,Diophantische Approximatien, Julius Springer, Berlin, (1936).

  10. [10]

    J. F. Koksma, Bewijs van een stelling over kettingbreuken,Mathematica A 6 (1937/38), 226–231.

  11. [11]

    J. F. Koksma, On continued fractions,Simon Stevin 29, (1951/52), 96–102.

  12. [12]

    C. Kraaikamp, The distribution of some sequences connected with the nearest integer continued fraction,Proc. Ned. Akad. van Wetensch.,A90 (1987), 177–191.

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Jager, H. Some metrical observations on the approximation of an irrational number by its nearest mediants. Period Math Hung 23, 5–16 (1991). https://doi.org/10.1007/BF02260389

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Key words and phrases

  • Continued fractions
  • Diophantine approximations