Florian Luca

activity

20242026

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4 papers · 1 filter

math.NT2024

Transcendence of Hecke-Mahler Series

Florian Luca, Joel Ouaknine, James Worrell

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 numbe…

cs.LO2024

On the Decidability of Presburger Arithmetic Expanded with Powers

Toghrul Karimov, Florian Luca, Joris Nieuwveld +2

We prove that for any integers $α, β > 1$ , the existential fragment of the first-order theory of the structure $⟨ Z; 0, 1, <, +, α^{N}, β^{N} ⟩$ …

math.NT2024

Transcendence for Pisot Morphic Words over an Algebraic Base

Pavol Kebis, Florian Luca, Joel Ouaknine +2

It is known that for a uniform morphic sequence $u = ⟨ u_{n} ⟩_{n = 0}^{\infty}$ and an algebraic number $β$ such that $∣ β ∣ > 1$ , the number $[\![\boldsymbol{u} ]\!]…

math.NT2024

Twisted rational zeros of linear recurrence sequences

Yuri Bilu, Florian Luca, Joris Nieuwveld +2

We introduce the notion of a twisted rational zero of a non-degenerate linear recurrence sequence (LRS). We show that any non-degenerate LRS has only finitely many such twisted rat…