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arXiv · 2406.19047

Linear independence of continued fractions with algebraic terms

Jaroslav Hančl·Mathias L. Laursen·Jitu Berhanu Leta
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Abstract

We give conditions on sequences of positive algebraic numbers $\{a_{n,j}\}_{n=1}^\infty$, $j=1,\dots ,M$ and number field $\mathbb K$ to ensure that the numbers defined by the continued fractions $[0;a_{1,j},a_{2,j},\dots ]$, $j=1,\dots ,M$ and $1$ are linearly independent over $\mathbb K$.

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Jaroslav Hančl, Mathias L. Laursen, Jitu Berhanu Leta. 2024-06-27. Linear independence of continued fractions with algebraic terms. https://arxiv.org/abs/2406.19047

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