Lamia Dammak, Mohamed Hbaib, Sonda Miladi: Transcendence criteria for non quadratic Ruban continued fractions in $\mathbb{Q}_p$, 79-90

Abstract:

The central objective of this work is to establish a new transcendence criterion for non quadratic $p$-adic numbers by using their Ruban continued fractions. By taking a pair $(\alpha, \alpha^{'})$ of $p$-adic numbers and under certain combinatorial conditions, we prove that one of $\alpha$ and $\alpha^{'}$ is transcendental or both are quadratic.

Key Words: Ruban continued fractions, $p$-adic numbers, subspace theorem, transcendence.

2020 Mathematics Subject Classification: 11A55, 11D88, 11J81.

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