Transcendental $p$-adic continued fractions
Number Theory
2017-12-07 v3
Abstract
We establish a new transcendence criterion of -adic continued fractions which are called Ruban continued fractions. By this result, we give explicit transcendental Ruban continued fractions with bounded -adic absolute value of partial quotients. This is -adic analogy of Baker's result. We also prove that -adic analogy of Lagrange Theorem for Ruban continued fractions is not true.
Cite
@article{arxiv.1407.0832,
title = {Transcendental $p$-adic continued fractions},
author = {Tomohiro Ooto},
journal= {arXiv preprint arXiv:1407.0832},
year = {2017}
}
Comments
11 pages, to appear in Math. Z