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arXiv · 1407.0832

Transcendental $p$-adic continued fractions

Tomohiro Ooto
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Abstract

We establish a new transcendence criterion of $p$-adic continued fractions which are called Ruban continued fractions. By this result, we give explicit transcendental Ruban continued fractions with bounded $p$-adic absolute value of partial quotients. This is $p$-adic analogy of Baker's result. We also prove that $p$-adic analogy of Lagrange Theorem for Ruban continued fractions is not true.

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Tomohiro Ooto. 2017-02-13. Transcendental $p$-adic continued fractions. https://doi.org/10.1007/s00209-017-1859-2

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