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arXiv · 2412.07908

Transcendence of Hecke-Mahler Series

Florian Luca·Joel Ouaknine·James Worrell
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Abstract

We prove transcendence of the Hecke-Mahler series $\sum_{n=0}^\infty f(\lfloor n\theta+\alpha \rfloor) \beta^{-n}$, where $f(x) \in \mathbb{Z}[x]$ is a non-constant polynomial $\alpha$ is a real number, $\theta$ is an irrational real number, and $\beta$ is an algebraic number such that $|\beta|>1$.

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Florian Luca, Joel Ouaknine, James Worrell. 2024-12-10. Transcendence of Hecke-Mahler Series. https://arxiv.org/abs/2412.07908

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