# 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 language English 1-16 16 International Journal of Number Theory https://doi.org/10.1142/S1793042118501440 Accepted/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

In: International Journal of Number Theory, 26.06.2018, p. 1-16.

Research output: Contribution to journalArticle

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