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Sur le développement en fractions continues a quotients partiels impairs

On the development of continued fractions with odd partial quotients

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Abstract

Let (B n ) n be the sequence of denominators of convergents, given by the continued fraction expansion with odd partial quotients of an irrational number. For integersm>2 andk, 0≤k<m, we give (almost everywhere) the density of the set of integersn such thatB n is congruent tok modm. This result comes from an ergodic system.

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Bibliographie

  1. Apostol, T. M.: Introduction to Analytic Number Theory. New-York-Heidelberg-Berlin: Springer. 1976.

    Google Scholar 

  2. Barbolosi, D.: Fractions continues à quotients partiels impairs, propriétés arithmétiques et ergodiques. Marseille: These d'Université de Provence. 1988.

  3. Jager, H., Liardet, P.: Distributions arithmétiques des dénominateurs de convergents de fractions continues. Indag. Math.50, 181–197 (1988).

    Google Scholar 

  4. Liardet, P.: Propriétés génériques de processus croisés. Israel J. Math.39, 303–325 (1981).

    Google Scholar 

  5. Rieger, G. J.: Über die Länge von Kettenbrüchen mit ungeraden Teilnennern. Abh. Braunschweig. Wiss. Ges.32, 61–69 (1981).

    Google Scholar 

  6. Rieger, G. J.: Ein Heilbronn-Satz für Kettenbrüche mit ungeraden Teilnennern. Math. Nachr.101, 295–307 (1981).

    Google Scholar 

  7. Rieger, G. J.: On the metrical theory of the continued fraction with odd partial quotients. Topics in Classical Number Theory, II, 1371–1418. (Budapest, 1981), Colloq. Math. Soc. János Bolyai34. Amsterdam-Oxford-New York: North Holland. 1984.

    Google Scholar 

  8. Schweiger, F.: Continued fractions with odd and even partial quotients. Arbeitsbericht Math. Inst. der Univ. Salzburg4, 59–70 (1982).

    Google Scholar 

  9. Schweiger, F.: A theorem of Kuzmin Levy type for continued fractions with odd partial quotients. Ibid.4, 45–50 (1982).

    Google Scholar 

  10. Schweiger, F.: On the approximation by continued fractions with odd and even partial quotients. Ibid.1–2, 105–114 (1984).

    Google Scholar 

  11. Shimura, G.: Introduction to the Arithmetic Theory of Automorphic Functions. Publ. of the Math. Soc. of Japan11. Princeton: University Press. 1971.

    Google Scholar 

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Authors and Affiliations

  1. Groupe Théorie Ergodique des Nombrwes, case 96, Université de Provence, 3, place Victor Hugo, F-13331, Marseille Cedex 3, France

    D. Barbolosi

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  1. D. Barbolosi
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Recherche partiellement subventionnée par l'URA no225, CNRS, Marseille.

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Barbolosi, D. Sur le développement en fractions continues a quotients partiels impairs. Monatshefte für Mathematik 109, 25–37 (1990). https://doi.org/10.1007/BF01298850

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  • DOI: https://doi.org/10.1007/BF01298850

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