Algebraic independence of power series generated by linearly independent positive numbers

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper we establish, using Mahler’s method, the algebraic independence of the values at an algebraic number of power series closely related to decimal expansion of linearly independent positive numbers. First we consider a simpler case in Theorem 1 and then generalize it to Theorem 3, which includes Nishioka’s result quoted as Theorem 2 of this paper. Lemma 7 plays an essential role in the proof of Theorems 1 and 3.

Original languageEnglish
Pages (from-to)367-380
Number of pages14
JournalResults in Mathematics
Volume46
Issue number3-4
DOIs
Publication statusPublished - 2004 Nov 1

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Algebraic Independence
Power series
Linearly
Theorem
Decimal expansion
Algebraic number
Lemma
Generalise

Keywords

  • Algebraic independence
  • Mahler’s method

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Applied Mathematics

Cite this

Algebraic independence of power series generated by linearly independent positive numbers. / Tanaka, Takaaki.

In: Results in Mathematics, Vol. 46, No. 3-4, 01.11.2004, p. 367-380.

Research output: Contribution to journalArticle

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