Algebraic independence of the values of the Hecke-Mahler series and its derivatives at algebraic numbers

Taka Aki Tanaka, Yusuke Tanuma

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We show that the Hecke-Mahler series, the generating function of the sequence {[nω]}n=1∞ for ω real, has the following property: Its values and its derivatives of any order, at any nonzero distinct algebraic numbers inside the unit circle, are algebraically independent if ω is a quadratic irrational number satisfying a suitable condition.

Original languageEnglish
Pages (from-to)2369-2384
Number of pages16
JournalInternational Journal of Number Theory
Volume14
Issue number9
DOIs
Publication statusPublished - 2018 Oct 1

Keywords

  • Algebraic independence
  • Hecke-Mahler series
  • Mahler's method

ASJC Scopus subject areas

  • Algebra and Number Theory

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