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On the metrical theory of a non-regular continued fraction expansion Cover
By: Dan Lascu and  George Cîrlig  
Open Access
|Apr 2017

References

  1. [1] Adams, W.W. and Davison, J.L., A remarkable class of continued fractions, Proc. Amer. Math. Soc. 65 (1977) 194-198.10.1090/S0002-9939-1977-0441879-4
  2. [2] Boyarsky, A. and Góra, P., Laws of Chaos: Invariant Measures and Dynamical Systems in One Dimension, Birkhäuser, Boston, 1997.10.1007/978-1-4612-2024-4
  3. [3] Brezinski, C., History of Continued Fractions and Padé Approximants. Springer Series in Computational Mathematics 12, Springer-Verlag, Berlin, 1991.10.1007/978-3-642-58169-4
  4. [4] Corless, R.M., Continued fractions and chaos, Amer. Math. Monthly 99(3) (1992), 203-215.10.1080/00029890.1992.11995835
  5. [5] Davison, J.L., A series and its associated continued fraction, Proc. Amer.Math. Soc.63(1) (1977) 29-32.10.1090/S0002-9939-1977-0429778-5
  6. [6] Iosifescu, M. and Kraaikamp C., Metrical theory of continued fractions, Kluwer Academic, 2002.10.1007/978-94-015-9940-5
  7. [7] Iosifescu, M. and Sebe, G.I., An exact convergence rate in a Gauss- Kuzmin-Lévy problem for some continued fraction expansion, in vol. Mathematical Analysis and Applications, 90-109. AIP Conf. Proc. 835 (2006), Amer.Inst.Physics, Melville, NY.10.1063/1.2205039
  8. [8] Kuzmin, R.O., On a problem of Gauss. Dokl. Akad. Nauk SSSR Ser. A (1928) 375-380. [Russian; French version in Atti Congr. Internaz.Mat. (Bologna, 1928), Tomo VI, pp.83-89. Zanichelli, Bologna, 1932].
  9. [9] Lascu, D., Markov processes in probabilistic number theory, Ph.D. thesis, Romanian Academy, 2010. (Romanian)
  10. [10] Lascu, D., On a Gauss-Kuzmin-type problem for a family of continued fraction expansions, J. Number Theory 133(7) (2013), 2153-2181.10.1016/j.jnt.2012.12.007
  11. [11] Lévy, P., Sur les lois de probabilité dont dépendent les quotients complets et incomplets d’une fraction continue. Bull. Soc. Math. France 57 (1929) 178-194.10.24033/bsmf.1150
  12. [12] Sebe, G.I., On convergence rate in the Gauss-Kuzmin problem for grotesque continued fractions, Monatsh. Math. 133 (2001), 241-254.10.1007/s006050170022
  13. [13] Sebe, G.I., A Gauss-Kuzmin theorem for the Rosen fractions, J.Théor.Nombres Bordx. 14 (2002), 667-682.10.5802/jtnb.381
  14. [14] Sebe, G.I. and Lascu, D. A Gauss-Kuzmin theorem and related questions for theta-expansions, arXiv preprint arXiv:1305.5563 (2013), 1-27.10.1155/2014/980461
DOI: https://doi.org/10.1515/auom-2015-0032 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 147 - 160
Submitted on: Oct 1, 2013
Accepted on: Dec 1, 2013
Published on: Apr 22, 2017
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2017 Dan Lascu, George Cîrlig, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.