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Matematicheskie Zametki, 2023, Volume 114, Issue 5, paper published in the English version journal (Mi mzm14030)  
Papers published in the English version of the journal

On the Maillet–Baker Ruban Continued Fractions in the $p$-Adic Field

B. Ammousa

a Department of Mathematics, Faculty of Sciences, University of Sfax
Abstract: We establish a transcendence criterion for a class of quasi-periodic Ruban $p$-adic continued fractions. We prove that a $p$-adic number whose partial quotients sequence is quasi-periodic and bounded in the $p$-adic field $\mathbb{Q}_p$ is either quadratic or transcendental.
Keywords: continued fraction, $p$-adic number, transcendence, subspace theorem.
Received: 12.05.2023
Revised: 13.07.2023
Published: 13.11.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 5, Pages 659–667
DOI: https://doi.org/10.1134/S0001434623110020
Bibliographic databases:
Document Type: Article
MSC: 11A55, 11D88, 11J81.
Language: English
Citation: B. Ammous, “On the Maillet–Baker Ruban Continued Fractions in the $p$-Adic Field”, Math. Notes, 114:5 (2023), 659–667
Citation in format AMSBIB
\Bibitem{Amm23}
\by B.~Ammous
\paper On the Maillet--Baker Ruban Continued Fractions in the $p$-Adic Field
\jour Math. Notes
\yr 2023
\vol 114
\issue 5
\pages 659--667
\mathnet{http://mi.mathnet.ru/mzm14030}
\crossref{https://doi.org/10.1134/S0001434623110020}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85187867268}
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