Florian Luca

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20242026

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math.NT2026

Multiplicative dependence in the sumset of multiplicative groups

Yuri Bilu, Florian Luca

Let $I^$ and $I^$ be finitely generated multiplicative groups of algebraic numbers such that $I^ \cap I^$ is a finite group. We show that, up to finitely many exceptions, non-zero su…

math.NT2025

On the growth of hypergeometric sequences

George Kenison, Jakub Konieczny, Florian Luca +3

Hypergeometric sequences obey first-order linear recurrence relations with polynomial coefficients and are commonplace throughout the mathematical and computational sciences. For c…

math.NT2025

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 $I^^{2}$ such that $∣ I^^{2} ∣ > 1$ , the number $[\![\boldsymbol{u} ]\…

math.NT2024

Transcendence of Hecke-Mahler Series

Florian Luca, Joel Ouaknine, James Worrell

We prove transcendence of the Hecke-Mahler series $\sum_{n=0}^\infty f(\lfloor nÎ¸+Î±\rfloor) Î²^{-n}$, where $f (x) \in Z [x]$ is a non-constant polynomial $I^\pm$ is a real n…