Linear independence of continued fractions with algebraic terms

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 $\mathbb K$.