On the quasi-periodic \(p\)-adic Ruban continued fractions. (English) Zbl 1538.11138
Summary: We study a family of quasi periodic \(p\)-adic Ruban continued fractions in the \(p\)-adic field \(\mathbb{Q}_p\) and we give a criterion of a quadratic or transcendental \(p\)-adic number which based on the \(p\)-adic version of the subspace theorem due to Schlickewei.
MSC:
| 11J70 | Continued fractions and generalizations |
| 11J61 | Approximation in non-Archimedean valuations |
| 11J81 | Transcendence (general theory) |
| 11J87 | Schmidt Subspace Theorem and applications |
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