Abstract:Continued fraction expansions provide a well-established bridge between algebraic properties of numbers and combinatorics on words. In this article, we investigate the algebraicity of $p$-adic numbers whose continued fractions arise from certain classes of words which generalize the classical automatic, periodic and palindromic words. Our main result shows that, under mild conditions on the $p$-adic continued fraction expansion, such numbers are either algebraic of degree at most 2 or transcendental. This result provides an analogue of results of Bugeaud and Adamczewski-Bugeaud in the real setting and extends previous works that were limited to specific choices of $p$-adic floor functions and less general classes of words.
From: Laura Capuano [view email]
[v1]
Thu, 20 Mar 2025 16:52:50 UTC (36 KB)
[v2]
Mon, 13 Jul 2026 14:59:46 UTC (44 KB)
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