Research PaperNo Access

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

Taka-aki Tanaka

Department of Mathematics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan

E-mail Address: [email protected]

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and

Yusuke Tanuma

Department of Mathematics, Keio University, Hiyoshi 3-14-1, Kohoku-ku, Yokohama 223-8522, Japan

E-mail Address: [email protected]

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https://doi.org/10.1142/S1793042118501440Cited by:1 (Source: Crossref)

Abstract

We show that the Hecke–Mahler series, the generating function of the sequence ${[n ω]}_{n = 1}^{\infty}$ 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.

Keywords:

AMSC: 11J85, 11J91

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