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Transcendence of Hecke-Mahler Series (2412.07908v2)
Published 10 Dec 2024 in math.NT and cs.FL
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 $|\beta|>1$.