Transcendental $p$-adic continued fractions

概要

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.

収録
Math. Z. 287, 1053–1064

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