Periodic continued fractions over $S$-integers in number fields and Skolem’s $p$-adic method
Bradley W. Brock, Noam D. Elkies, Bruce W. Jordan · Acta Arithmetica · 2020
We generalize the classical theory of periodic continued fractions (PCFs) over ${\mathbf Z}$ to rings $\mathcal O \subseteq \mathbf C $ of $S$-integers in a number field. If it exists, the limit of a PCF $P=[b_1,\ldots ,b_N,\overline {a_1,\ldots ,a_k}