Transcendence of Hecke–Mahler series

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-02-25 DOI:10.1112/blms.70033

Florian Luca, Joël Ouaknine, James Worrell

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引用次数: 0

Abstract

We prove transcendence of the Hecke–Mahler series $\sum_{n = 0}^{\infty} f (⌊ n θ + α ⌋) β^{- n}$ , where $f (x) \in Z [x]$ is a non-constant polynomial, $α$ is a real number, $θ$ is an irrational real number and $β$ is an algebraic number such that $| β | > 1$ .

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Hecke-Mahler系列的超越

证明了Hecke-Mahler级数∑n = 0∞f（⌊n θ）的超越性+ α⌋)β−n $\sum _{n=0}^\infty f(\lfloor n\theta +\alpha \rfloor) \beta ^{-n}$，式中f (x)∈Z [x] $f(x) \in \mathbb {Z}[x]$为非常多项式，α $\alpha$为实数，θ $\theta$是无理数，β $\beta$是代数数，使得| β | ＆gt；1 $|\beta |>1$。

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