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Transcendental p-adic continued fractions

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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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Acknowledgements

I am greatly indebted to Prof. Kenichiro Kimura for several helpful comments concerning the proof of main theorems. I also wish to express my gratitude to Prof. Masahiko Miyamoto.

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  1. Graduate School of Pure and Applied Sciences, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibaraki, 305-8571, Japan

    Tomohiro Ooto

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  1. Tomohiro Ooto
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Correspondence to Tomohiro Ooto.

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Ooto, T. Transcendental p-adic continued fractions. Math. Z. 287, 1053–1064 (2017). https://doi.org/10.1007/s00209-017-1859-2

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  • DOI: https://doi.org/10.1007/s00209-017-1859-2

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