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arXiv:1512.06511 [math.NT]AbstractReferencesReviewsResources

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

Tomohiro Ooto

Published 2015-12-21Version 1

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 is 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.

Comments: 12 pages. arXiv admin note: text overlap with arXiv:1512.04041
Categories: math.NT
Subjects: 11J61, 11J82, 11B85
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