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arXiv · 2604.01464

On algebraic independence of three p-adic continued fractions

Sarra Ahallal·Mohamed Begare·Ali Kacha
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Abstract

In this paper, we establish sufficient conditions on the elements of the p-adic continued fractions $A$ and $B$ which guarantee that the p-adic continued fractions $A, B $ and $A^{B}$ are algebraically independent over $\mathbb{Q}$. These elements have partial quotients that increase rapidly. We note that these results extend some work of Bundschuh. Furthermore, we give some numerical examples which illustrated the theoretical results.

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Sarra Ahallal, Mohamed Begare, Ali Kacha. 2026-04-01. On algebraic independence of three p-adic continued fractions. https://arxiv.org/abs/2604.01464

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