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Geometrization of the Fibonacci numeration system, with applications to number theory


Authors: E. P. Davlet′yarova, A. A. Zhukova and A. V. Shutov
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 25 (2013), nomer 6.
Journal: St. Petersburg Math. J. 25 (2014), 893-907
MSC (2010): Primary 11B39
DOI: https://doi.org/10.1090/S1061-0022-2014-01321-0
Published electronically: September 8, 2014
MathSciNet review: 3234837
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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.


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Additional 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

DOI: https://doi.org/10.1090/S1061-0022-2014-01321-0
Keywords: Fibonacci numeration system, geometrization theorem, ternary Goldbach problem
Received by editor(s): July 22, 2012
Published electronically: September 8, 2014
Additional Notes: Partially supported by RFBR (grant no. 11-01-00578-a)
Article copyright: © Copyright 2014 American Mathematical Society