G. Peruginelli

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math.NT2025

On the Lucas and Lehmer sequences in Dedekind domains

Xiumei Li, Giulio Peruginelli, Min Sha

In this paper, we first obtain the strong divisibility property for the Lucas and Lehmer sequences in Dedekind domains, and then establish analogues of Zsigmondy's theorem and the…

math.NT2025

Nontriviality of rings of integral-valued polynomials

Giulio Peruginelli, Nicholas J. Werner

Let $S$ be a subset of $Z$ , the ring of all algebraic integers. A polynomial $f \in Q [X]$ is said to be integral-valued on $S$ if $f(s) \in \overline{\ma…

math.NT2025

Stacked Pseudo-Convergent Sequences and Polynomial Dedekind Domains

Giulio Peruginelli

Let $p \in Z$ be a prime, $Q_{p}$ a fixed algebraic closure of the field of $p$ -adic numbers and $Z_{p}$ the absolute integral closure of th…