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

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.

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

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