We prove transcendence of the Hecke-Mahler series ∑n=0∞f(floor(nθ+α))β-n, where f(x) ∈ Z[x] is a non-constant polynomial, α is a real number, θ is an irrational number, and β is an algebraic number such that |β|>1.
Submitted, 2025. 8 pages.
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© 2025 Florian Luca, Joël Ouaknine, and James Worrell.