Geometrization of the Fibonacci numeration system, with applications to number theory
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E. P. Davlet′yarova, A. A. Zhukova and A. V. Shutov
Translated by: A. Plotkin - St. Petersburg Math. J. 25 (2014), 893-907
- DOI: https://doi.org/10.1090/S1061-0022-2014-01321-0
- Published electronically: September 8, 2014
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Abstract:
A geometrization theorem is obtained for the Fibonacci numeration system. As applications, several classical problems are solved concerning numbers that have a given tail of the expansion with respect to the Fibonacci numeration system.References
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Bibliographic Information
- E. P. Davlet′yarova
- Affiliation: Department of Mathematics and Physics, Vladimir State University, Gorkiĭ str. 87, Vladimir 600000, Russia
- Email: anele_p@mail.ru
- A. A. Zhukova
- Affiliation: Department of Management, Vladimir Branch, President RF Academy of National Economy and State Service, Gorkiĭ str. 59a, Vladimir 600017, Russia
- Email: georg967@mail.ru
- A. V. Shutov
- Affiliation: Department of Mathematics and Physics, Vladimir State University, Gorkiĭ str. 87, Vladimir 600000, Russia
- Email: a1981@mail.ru
- Received by editor(s): July 22, 2012
- Published electronically: September 8, 2014
- Additional Notes: Partially supported by RFBR (grant no. 11-01-00578-a)
- © Copyright 2014 American Mathematical Society
- Journal: St. Petersburg Math. J. 25 (2014), 893-907
- MSC (2010): Primary 11B39
- DOI: https://doi.org/10.1090/S1061-0022-2014-01321-0
- MathSciNet review: 3234837