Mahler's classification and a certain class of $p$-adic numbers

Tomohiro Ooto

Mahler's classification and a certain class of $p$-adic numbers

Number Theory 2017-02-23 v3

Authors: Tomohiro Ooto

Abstract

In this paper, we study a relation between digits of $p$ -adic numbers and Mahler's classification. We show that an irrational $p$ -adic number whose digits are automatic, primitive morphic, or Sturmian is an $S$ -, $T$ -, or $U_1$ -number in the sense of Mahler's classification. Furthermore, we give an algebraic independence criterion for $p$ -adic numbers whose digits are Sturmian.

Keywords

Mahler's classification p-adic numbers automatic digits primitive morphic Sturmian algebraic independence digit sequences

Cite

@article{arxiv.1512.06511,
  title  = {Mahler's classification and a certain class of $p$-adic numbers},
  author = {Tomohiro Ooto},
  journal= {arXiv preprint arXiv:1512.06511},
  year   = {2017}
}

Comments

12 pages. arXiv admin note: text overlap with arXiv:1512.04041

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