Papers published in the English version of the journal

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

B. Ammous<sup>a

a</sup> 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.

MSC: 11A55, 11D88, 11J81.

Received: 12.05.2023
Revised: 13.07.2023

Language: English

 English version: Mathematical Notes, 2023, 114:5, 659–667

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