Florian Luca

activity

20242026

collaborators

6 papers

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…

cs.DM2026

Conjectural Decidability of the Skolem Problem

Florian Luca, JoÃ«l Ouaknine, James Worrell

The Skolem Problem asks to determine whether a given integer linear recurrence sequence (LRS) has a zero term. This problem, whose decidability has been open for many decades, aris…

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…

cs.LO2025

On the Decidability of Presburger Arithmetic Expanded with Powers

Toghrul Karimov, Florian Luca, Joris Nieuwveld +2

We prove that for any integers $I^\pm, I^^{2} > 1$ , the existential fragment of the first-order theory of the structure $\langle \mathbb{Z}; 0,1,<, +, Î±^{\mathbb{N}}, Î²^{\mathbb{N}}\rang…

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…