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

Takaaki Tanaka, Yusuke Tanuma

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We show that the Hecke–Mahler series, the generating function of the sequence (Formula presented.) for (Formula presented.) 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 (Formula presented.) is a quadratic irrational number satisfying a suitable condition.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalInternational Journal of Number Theory
DOIs
Publication statusAccepted/In press - 2018 Jun 26

Fingerprint

Algebraic Independence
Algebraic number
Derivative
Series
Irrational number
Unit circle
Generating Function
Distinct

Keywords

  • Algebraic independence
  • Hecke–Mahler series
  • Mahler’s method

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

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