@article{eca25e2a01c249ce9938bd4ec4a69dcf,
title = "Algebraic independence of the values of the Hecke-Mahler series and its derivatives at algebraic numbers",
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.",
keywords = "Algebraic independence, Hecke-Mahler series, Mahler's method",
author = "Tanaka, {Taka Aki} and Yusuke Tanuma",
note = "Funding Information: The authors are grateful to the anonymous referee for careful reading and insightful comments that improved this paper. This work was supported by JSPS KAKENHI Grant Number 15K04792. Publisher Copyright: {\textcopyright} 2018 World Scientific Publishing Company.",
year = "2018",
month = oct,
day = "1",
doi = "10.1142/S1793042118501440",
language = "English",
volume = "14",
pages = "2369--2384",
journal = "International Journal of Number Theory",
issn = "1793-0421",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "9",
}