Florian Luca

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20242026

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math.NT2026

On the Divisibility Relation $σ (n) ∣ σ (n + h)$ and a Generalized Erdős--Sierpiński Conjecture

Amirali Fatehizadeh, Florian Luca

For each fixed positive integer $h$ , we study the divisibility relation $σ (n) ∣ σ (n + h)$ . We isolate an explicit regular family arising from integral quotients of shifted abundancy…

math.NT2026

Multiplicative dependence in the sumset of multiplicative groups

Yuri Bilu, Florian Luca

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

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.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…

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} ]\!]…

On the Divisibility Relation σ(n)∣σ(n+h) and a Generalized Erdős--Sierpiński Conjecture

Multiplicative dependence in the sumset of multiplicative groups

On the growth of hypergeometric sequences

Transcendence of Hecke-Mahler Series

Transcendence for Pisot Morphic Words over an Algebraic Base

On the Divisibility Relation $σ (n) ∣ σ (n + h)$ and a Generalized Erdős--Sierpiński Conjecture